Electrical Energy

What Is Electrical Energy?

Electrical energy is energy transferred by moving electric charges or by charges moving through a potential difference.

Electrical circuits allow energy to be transferred from an energy source to electrical devices.

For example:

battery → electrical transfer → lamp → light + thermal energy

The battery does not "create" energy. It transfers energy from its chemical energy store through the electrical circuit.

The SI unit of energy is the:

joule (J)

---

Electrical Energy Transfer

When charge moves through a potential difference, energy is transferred.

Potential difference is defined as:

V = E/Q

Rearranging:

E = QV

where:

• E = energy transferred (J)
• Q = charge (C)
• V = potential difference (V)

This means:

1 V = 1 J/C

A potential difference of 1 V transfers 1 J of energy for every coulomb of charge passing through the component.

---

Example: Energy per Charge

A charge of 5 C moves through a potential difference of 12 V.

E = QV

E = 5 × 12

E = 60 J

Therefore, 60 J of energy is transferred.

---

Connecting Energy to Current

Current is:

I = Q/t

Therefore:

Q = It

Substitute this into:

E = QV

to obtain:

E = VIt

This is one of the most important equations for electrical energy.

where:

• E = energy transferred (J)
• V = potential difference (V)
• I = current (A)
• t = time (s)

---

Electrical Energy Equation

The main equation is:

E = VIt

This tells us that electrical energy transfer depends on:

• voltage
• current
• time

Increasing any of these generally increases the amount of energy transferred.

---

Worked Example

A heater operates at:

V = 230 V

I = 5 A

t = 60 s

Energy transferred:

E = VIt

E = 230 × 5 × 60

E = 69,000 J

or:

E = 69 kJ

---

Electrical Power

Power is the rate at which energy is transferred.

Power is represented by:

P

and measured in:

watts (W)

The relationship is:

P = E/t

Therefore:

E = Pt

Since:

P = VI

we obtain:

E = VIt

So these equations are closely connected.

---

What Does One Watt Mean?

One watt means:

1 W = 1 J/s

Therefore, a 100 W device transfers:

100 J every second

If it operates for 10 seconds:

E = Pt

E = 100 × 10

E = 1000 J

---

Comparing Power and Energy

Power and energy are related but are not the same quantity.

Energy tells us the total amount transferred.

Power tells us how quickly the energy is transferred.

For example:

A 2000 W heater transfers energy much faster than a 100 W lamp.

However, a low-power device operating for a long time can transfer more total energy than a high-power device operating briefly.

---

Example: Same Energy, Different Power

Device A:

P = 100 W

t = 100 s

E = Pt

E = 100 × 100

E = 10,000 J

Device B:

P = 1000 W

t = 10 s

E = 1000 × 10

E = 10,000 J

Both transfer the same total energy.

Device B transfers it much faster.

---

Energy Transformations

Electrical devices transfer electrical energy into other forms.

Common transformations include:

Lamp

electrical → light + thermal

Heater

electrical → thermal

Motor

electrical → kinetic + thermal + sound

Speaker

electrical → sound + thermal

Television

electrical → light + sound + thermal

Battery being charged

electrical → chemical energy store

In real devices, some energy is usually transferred in ways that are not useful for the intended purpose.

---

Conservation of Energy

The law of conservation of energy states:

Energy cannot be created or destroyed.

Energy can:

• be transferred
• be transformed
• move between energy stores

Therefore:

total energy before = total energy after

For an electrical device:

electrical energy input = useful energy output + unwanted energy transfers

---

Example: Lamp

Suppose a lamp receives:

100 J

of electrical energy.

It transfers:

20 J as useful light

and:

80 J as thermal energy.

Energy conservation gives:

100 = 20 + 80

100 J = 100 J

No energy has disappeared.

The thermal transfer may be unwanted, but the energy is still conserved.

---

Useful and Wasted Energy

The term wasted energy is commonly used to describe energy transferred in a way that is not useful for the intended purpose.

However, the energy is not destroyed.

For example, a motor may transfer electrical energy into:

• useful kinetic energy
• unwanted thermal energy
• unwanted sound energy

The thermal and sound transfers reduce the amount available for the desired output.

---

Efficiency

Efficiency compares useful energy output with total energy input.

efficiency = useful energy output / total energy input

As a percentage:

efficiency = useful energy output / total energy input × 100%

Efficiency can also be calculated using power:

efficiency = useful power output / total power input × 100%

---

Efficiency Example

A motor receives:

500 J

of electrical energy.

It transfers:

400 J

into useful kinetic energy.

Efficiency:

efficiency = 400/500 × 100%

efficiency = 80%

The remaining:

500 − 400 = 100 J

is transferred in unwanted forms such as thermal and sound energy.

---

Comparing Electrical Devices

Devices can be compared using:

• power
• total energy consumption
• efficiency
• operating time
• useful output
• cost of operation

A device with a lower power rating does not automatically use less energy in every situation.

Operating time must also be considered.

---

Example: Comparing Two Heaters

Heater A:

P = 1500 W

operates for 20 minutes.

Heater B:

P = 1000 W

operates for 40 minutes.

Convert time to seconds.

Heater A:

20 min = 1200 s

E_A = Pt

E_A = 1500 × 1200

E_A = 1,800,000 J

Heater B:

40 min = 2400 s

E_B = 1000 × 2400

E_B = 2,400,000 J

Although Heater B has lower power, it transfers more total energy because it operates for longer.

---

Energy in Resistors

For a resistor:

P = I²R

Since:

E = Pt

we obtain:

E = I²Rt

Another power equation is:

P = V²/R

Therefore:

E = V²t/R

So electrical energy transferred by a resistor can be calculated using:

E = VIt

E = I²Rt

or:

E = V²t/R

Choose the equation that matches the known quantities.

---

Worked Resistor Example

A 10 Ω resistor carries:

I = 2 A

for:

t = 30 s

Use:

E = I²Rt

E = 2² × 10 × 30

E = 4 × 10 × 30

E = 1200 J

Most of this energy is transferred as thermal energy.

---

Electrical Heating

When current passes through a resistor, electrical energy is transferred into thermal energy.

This is often called:

Joule heating

It occurs because moving charge carriers interact with the material through which they move.

Electrical heating is useful in:

• kettles
• toasters
• ovens
• hair dryers
• electric heaters

In these devices, thermal energy is the intended output.

---

Heating Can Also Be Unwanted

Electrical heating is not always useful.

Energy may be transferred unnecessarily in:

• wires
• motors
• batteries
• electronic components
• power transmission lines

This reduces efficiency.

For resistance R carrying current I:

P_loss = I²R

This is why large currents can cause significant heating.

---

Electrical Energy in a Battery

A battery transfers energy from a chemical energy store.

If a battery has an emf ε and charge Q passes through it:

E = εQ

For example, if:

ε = 12 V

Q = 50 C

then:

E = 12 × 50

E = 600 J

The battery supplies approximately 600 J of energy.

---

Energy in a Real Battery

A real battery has internal resistance.

The total power supplied by the battery is:

P_source = εI

Useful power delivered to the external circuit is:

P_external = VI

Power transferred internally is:

P_internal = I²r

Therefore:

εI = VI + I²r

This is another example of conservation of energy.

---

Energy Transfer in a Motor

An electric motor converts electrical energy mainly into mechanical energy.

However, some energy is also transferred as:

• thermal energy
• sound
• vibration

For example:

electrical input = 1000 J

useful mechanical output = 850 J

unwanted transfers = 150 J

Efficiency:

850/1000 × 100%

= 85%

---

Energy Transfer in a Lamp

Different types of lamps can provide similar amounts of light while using different amounts of electrical energy.

An inefficient lamp may transfer a large proportion of its input energy into unwanted thermal energy.

A more efficient lamp transfers a greater proportion into useful light.

This is why power alone is not enough when comparing devices.

We should also consider the useful output produced.

---

Comparing Lamps

Suppose two lamps provide approximately the same useful light output.

Lamp A:

P = 60 W

Lamp B:

P = 10 W

If both operate for 5 hours, Lamp B uses much less electrical energy.

Lamp A:

E = 60 × 5

= 300 Wh

Lamp B:

E = 10 × 5

= 50 Wh

Lamp B uses:

1/6 as much energy

over the same period.

---

Joules and Kilowatt-Hours

The joule is the SI unit of energy, but household electrical energy consumption is often measured in:

kilowatt-hours (kWh)

A kilowatt-hour is a unit of energy, not power.

1 kWh = 1000 W × 3600 s

Therefore:

1 kWh = 3,600,000 J

or:

1 kWh = 3.6 MJ

---

Calculating Energy in kWh

When power is measured in kilowatts and time in hours:

E = Pt

gives energy directly in kWh.

For example:

P = 2 kW

t = 3 h

E = 2 × 3

E = 6 kWh

---

Converting Watts to Kilowatts

Remember:

1000 W = 1 kW

Therefore:

500 W = 0.5 kW

2000 W = 2 kW

75 W = 0.075 kW

This conversion is important when calculating energy consumption in kWh.

---

Household Energy Example

A 1500 W heater operates for 4 hours.

Convert power:

1500 W = 1.5 kW

Then:

E = Pt

E = 1.5 × 4

E = 6 kWh

In joules:

E = 6 × 3.6 MJ

E = 21.6 MJ

---

Cost of Electrical Energy

Electricity bills are commonly based on the amount of energy consumed.

If:

energy used = 6 kWh

electricity price = $0.30 per kWh

then:

cost = 6 × 0.30

cost = $1.80

The general relationship is:

cost = energy used × price per unit of energy

---

Comparing Appliance Energy Use

Suppose a television uses:

150 W

for:

4 hours

Energy:

0.150 × 4

= 0.60 kWh

A 2000 W kettle operates for:

6 minutes

Convert:

2000 W = 2 kW

6 min = 0.10 h

Energy:

2 × 0.10

= 0.20 kWh

Even though the kettle has much greater power, the television uses more energy in this example because it operates for much longer.

---

Standby Energy Use

Some electrical devices continue consuming power even when they are not actively being used.

Suppose a device uses:

5 W

in standby for 24 hours.

Convert:

5 W = 0.005 kW

Energy:

E = 0.005 × 24

E = 0.12 kWh

For one device this may seem small, but repeated over long periods and many devices it can become significant.

---

Energy Flow Diagrams

Energy transfers can be represented using an energy flow diagram.

For an electric motor:

electrical energy input

→ useful kinetic energy

• thermal energy
• sound energy

For an electric heater:

electrical energy input

→ useful thermal energy

The usefulness of an energy transfer depends on the purpose of the device.

---

Useful Energy Depends on Purpose

Thermal energy from a lamp may be considered unwanted.

Thermal energy from a heater is useful.

Sound from an electric motor may be unwanted.

Sound from a speaker is useful.

Therefore, whether an energy output is considered useful depends on the intended function of the device.

---

Sankey Diagrams

A Sankey diagram represents energy transfers using arrows.

The width of each arrow represents the amount of energy transferred.

A device might receive:

100 J electrical energy

and transfer:

70 J useful energy

30 J unwanted thermal energy

The input arrow represents 100 J and splits into outputs representing 70 J and 30 J.

Sankey diagrams make it easier to compare useful and unwanted energy transfers visually.

---

Conservation of Energy in a Circuit

Consider a battery supplying two resistors.

The battery supplies:

E_source

The resistors transfer:

E₁

and:

E₂

Conservation of energy requires:

E_source = E₁ + E₂

Similarly, Kirchhoff's Voltage Law states:

V_source = V₁ + V₂

These ideas are closely related because voltage represents energy transferred per unit charge.

---

Voltage and Energy Conservation

Suppose 2 C of charge passes through a 12 V battery.

Energy supplied:

E = QV

E = 2 × 12

E = 24 J

The charge then passes through two components with voltage drops:

4 V

and:

8 V

First component:

E₁ = 2 × 4

E₁ = 8 J

Second component:

E₂ = 2 × 8

E₂ = 16 J

Total:

8 + 16 = 24 J

The energy transferred by the components equals the energy supplied by the source.

---

Choosing an Energy-Efficient Device

When comparing devices, consider:

• useful output
• input power
• operating time
• total energy consumption
• efficiency
• expected lifetime
• required performance

A lower-power device may be preferable if it produces the same useful output.

However, comparing only power ratings can be misleading if the devices perform different amounts of useful work.

---

Example: Comparing Two Motors

Motor A:

input power = 500 W

useful output power = 400 W

Efficiency:

400/500 × 100%

= 80%

Motor B:

input power = 450 W

useful output power = 405 W

Efficiency:

405/450 × 100%

= 90%

Motor B has:

• lower input power
• greater useful output
• greater efficiency

For this operating condition, Motor B performs better energetically.

---

Reducing Electrical Energy Waste

Electrical energy waste can often be reduced by:

• using efficient devices
• reducing unnecessary operating time
• switching off unused equipment
• reducing unwanted resistance
• improving insulation in heating systems
• reducing friction in motors
• maintaining electrical equipment
• choosing devices appropriate for the required task

Energy conservation does not mean efficiency is automatically high.

Energy is always conserved, but it may be transferred into unwanted forms.

---

Electrical Energy and Power Transmission

Power losses in wires can be calculated using:

P_loss = I²R

For the same transmitted power, using a higher voltage allows a lower current.

Since heating losses depend on I²:

lower current → much lower heating losses

This is why electrical power is transmitted over long distances at high voltages.

---

Common Mistakes

Mistake: Confusing energy and power.
Energy is the total amount transferred; power is the rate of transfer.

Mistake: Saying energy is used up or destroyed.
Energy is conserved but may be transferred into less useful forms.

Mistake: Forgetting time in energy calculations.
Power alone does not determine total energy consumption.

Mistake: Using minutes with power in watts without converting.
For E in joules using E = Pt, time should normally be in seconds.

Mistake: Treating kWh as a unit of power.
The kilowatt-hour is a unit of energy.

Mistake: Using watts directly with hours and calling the answer kWh.
Convert watts to kilowatts first.

Mistake: Assuming the highest-power device always uses the most energy.
Operating time must also be considered.

Mistake: Calling unwanted energy "lost" as though it disappears.
It is transferred to other stores or surroundings.

Mistake: Assuming thermal energy is always wasted.
For a heater, thermal energy is the intended useful output.

---

Key Terms

Electrical energy — energy transferred through electrical processes involving moving charge and potential differences.

Energy transfer — movement of energy from one store or system to another.

Joule (J) — SI unit of energy.

Power — rate of energy transfer.

Watt (W) — unit of power equal to one joule per second.

Potential difference — energy transferred per unit charge.

Efficiency — fraction of input energy or power transferred usefully.

Useful energy — energy transferred in the intended way.

Unwanted energy transfer — energy transferred in a way that does not contribute to the intended purpose.

Kilowatt-hour (kWh) — energy transferred by 1 kW of power operating for one hour.

Joule heating — transfer of electrical energy into thermal energy due to resistance.

Energy transformation — change from one form or store of energy to another.

Conservation of energy — principle that energy cannot be created or destroyed.

Sankey diagram — diagram in which arrow widths represent amounts of energy transferred.

---

Key Takeaways

• Electrical energy is transferred when charge moves through a potential difference.
• The SI unit of energy is the joule.
• Energy transferred by charge can be calculated using E = QV.
• Since Q = It, electrical energy can also be calculated using E = VIt.
• Power is the rate of energy transfer.
• P = E/t and therefore E = Pt.
• Electrical power can be calculated using P = VI.
• For resistors, energy can also be calculated using E = I²Rt or E = V²t/R.
• Electrical devices transform energy into different useful and unwanted forms.
• Energy is never destroyed.
• Conservation of energy requires total input energy to equal total output energy.
• Efficiency measures the proportion of energy transferred usefully.
• Power and energy are different quantities.
• A high-power device transfers energy rapidly but may not necessarily consume more total energy.
• Operating time is essential when comparing energy consumption.
• The kilowatt-hour is a unit of energy.
• 1 kWh = 3.6 MJ.
• Electrical energy cost depends on both energy consumption and the price per unit.
• Sankey diagrams can represent useful and unwanted energy transfers.
• Real electrical devices are less than 100% efficient because some energy is transferred in unwanted ways.
• Comparing devices should consider power, operating time, useful output, energy consumption and efficiency.

Check Your Understanding

1. Define electrical energy.
2. What is the SI unit of energy?
3. Explain the meaning of E = QV.
4. A charge of 8 C moves through a potential difference of 6 V. Calculate the energy transferred.
5. Write the equation relating electrical energy, voltage, current and time.
6. A 12 V device draws 2 A for 30 s. Calculate the energy transferred.
7. Explain the difference between energy and power.
8. What does it mean if a device has a power rating of 500 W?
9. A 1500 W heater operates for 10 minutes. Calculate the energy transferred in joules.
10. A 10 Ω resistor carries 3 A for 20 s. Calculate the energy transferred using E = I²Rt.
11. State the law of conservation of energy.
12. A motor receives 1000 J and transfers 750 J into useful mechanical energy. Calculate its efficiency.
13. What happens to the remaining 250 J in Question 12?
14. Explain why thermal energy from a lamp may be unwanted while thermal energy from a heater is useful.
15. Convert 2.5 kWh into joules.
16. A 2 kW heater operates for 3 hours. Calculate its energy consumption in kWh.
17. A 100 W device operates for 10 hours while a 1000 W device operates for 30 minutes. Which transfers more electrical energy?
18. Explain why a lower-power device does not necessarily consume less energy.
19. Describe the energy transformations occurring in an electric motor.
20. Explain how energy conservation, efficiency, power and operating time can be used together to compare two electrical devices.

Electrical Power

What Is Electrical Power?

Electrical power is the rate at which electrical energy is transferred or transformed.

In other words, power tells us how quickly energy is being transferred.

The basic equation is:

P = E/t

where:

• P = power (W)
• E = energy transferred (J)
• t = time (s)

The SI unit of power is the watt (W).

1 W = 1 J/s

Therefore, a 100 W device transfers 100 J of energy every second.

---

Power Is Not Energy

Power and energy are closely related, but they are not the same quantity.

Energy measures the total amount transferred.

Power measures how quickly that transfer occurs.

For example:

A 2000 W kettle transfers energy much faster than a 10 W LED lamp.

However, if the LED operates for a very long time, it can eventually transfer more total energy than the kettle.

The relationship is:

E = Pt

---

Understanding the Watt

Because:

1 W = 1 J/s

a device rated at 500 W transfers:

500 J every second

A 2000 W heater transfers:

2000 J every second

or:

2 kJ every second

Higher power means a faster rate of energy transfer.

---

Basic Power Calculation

A device transfers:

E = 6000 J

in:

t = 30 s

Power:

P = E/t

P = 6000/30

P = 200 W

The device transfers energy at a rate of 200 J each second.

---

Electrical Power from Voltage and Current

Electrical energy is:

E = VIt

Since:

P = E/t

substitute:

P = VIt/t

Therefore:

P = VI

where:

• P = electrical power (W)
• V = potential difference (V)
• I = current (A)

This is one of the most important equations in electrical circuits.

---

Example Using P = VI

An appliance operates at:

V = 230 V

I = 4 A

Power:

P = VI

P = 230 × 4

P = 920 W

The appliance transfers electrical energy at a rate of 920 J/s.

---

Calculating Current from Power

Rearrange:

P = VI

to obtain:

I = P/V

Suppose a 1200 W appliance operates at 240 V.

I = 1200/240

I = 5 A

---

Calculating Voltage from Power

Rearrange:

P = VI

to obtain:

V = P/I

Suppose:

P = 600 W

I = 5 A

Then:

V = 600/5

V = 120 V

---

Power in Resistors

For a resistor:

P = VI

Using Ohm's Law:

V = IR

we can derive other power equations.

Substitute V = IR into P = VI:

P = (IR)I

Therefore:

P = I²R

This equation is particularly useful when current and resistance are known.

---

Example Using P = I²R

A 20 Ω resistor carries:

I = 3 A

Power:

P = I²R

P = 3² × 20

P = 9 × 20

P = 180 W

---

Another Power Equation

Ohm's Law also gives:

I = V/R

Substitute this into:

P = VI

P = V(V/R)

Therefore:

P = V²/R

This equation is useful when voltage and resistance are known.

---

Example Using P = V²/R

A resistor has:

R = 50 Ω

and:

V = 100 V

Power:

P = V²/R

P = 100²/50

P = 10,000/50

P = 200 W

---

The Three Main Electrical Power Equations

For suitable circuit situations:

P = VI

P = I²R

P = V²/R

Choose the equation based on the quantities provided.

---

Choosing the Correct Equation

Suppose a question gives:

V = 12 V

R = 6 Ω

You could first calculate current:

I = V/R

I = 12/6

I = 2 A

Then:

P = VI

P = 12 × 2

P = 24 W

Or calculate directly:

P = V²/R

P = 12²/6

P = 144/6

P = 24 W

Both methods agree.

---

Power Ratings

Electrical devices usually have a power rating.

Examples might include:

• LED lamp: 10 W
• television: 100 W
• refrigerator: 150 W while running
• hair dryer: 1800 W
• kettle: 2000 W

The power rating indicates the rate at which the device is designed to transfer energy under its rated operating conditions.

---

Reading an Appliance Rating

Suppose an appliance is labelled:

230 V, 1150 W

This tells us:

rated voltage = 230 V

rated power = 1150 W

The expected current can be estimated:

I = P/V

I = 1150/230

I = 5 A

This information can help determine appropriate:

• wiring
• switches
• circuit protection
• power supplies

---

What Does a 2000 W Rating Mean?

A 2000 W appliance transfers energy at approximately:

2000 J/s

when operating at its rated conditions.

If it operates for 10 seconds:

E = Pt

E = 2000 × 10

E = 20,000 J

If it operates for 60 seconds:

E = 2000 × 60

E = 120,000 J

or:

120 kJ

---

Power and Operating Time

Power alone does not determine total energy consumption.

Energy is:

E = Pt

Therefore, both:

• power
• operating time

must be considered.

A low-power device operating continuously may consume more energy than a high-power device used briefly.

---

Comparing Two Appliances

Appliance A:

P = 2000 W

operates for:

5 minutes

Appliance B:

P = 200 W

operates for:

2 hours

Appliance A

5 min = 300 s

E = Pt

E = 2000 × 300

E = 600,000 J

Appliance B

2 h = 7200 s

E = 200 × 7200

E = 1,440,000 J

Although Appliance A has ten times the power, Appliance B transfers more total energy because it operates much longer.

---

Power and Energy Consumption

Household electrical energy is commonly measured in:

kilowatt-hours (kWh)

Convert power into kilowatts:

1000 W = 1 kW

Then use:

E = Pt

with:

• P in kW
• t in hours
• E in kWh

---

Example in Kilowatt-Hours

A 2 kW heater operates for:

3 h

Energy:

E = Pt

E = 2 × 3

E = 6 kWh

Since:

1 kWh = 3.6 MJ

the energy is also:

6 × 3.6

= 21.6 MJ

---

Comparing Appliance Energy Consumption

Consider two appliances.

Kettle

Power:

2.0 kW

Operating time:

0.10 h

Energy:

E = 2.0 × 0.10

E = 0.20 kWh

Television

Power:

0.15 kW

Operating time:

4 h

Energy:

E = 0.15 × 4

E = 0.60 kWh

Although the kettle is much more powerful, the television consumes more energy in this example because it operates for longer.

---

Calculating Operating Cost

If electricity is charged per kilowatt-hour:

cost = energy used × price per kWh

Suppose a 1.5 kW heater operates for 4 hours.

Energy:

E = 1.5 × 4

E = 6 kWh

If electricity costs:

$0.30/kWh

then:

cost = 6 × 0.30

cost = $1.80

---

Daily and Monthly Energy Use

A 100 W device operates for 8 hours each day.

Convert:

100 W = 0.100 kW

Daily energy:

E = 0.100 × 8

E = 0.80 kWh

For 30 days:

E = 0.80 × 30

E = 24 kWh

If electricity costs $0.30/kWh:

cost = 24 × 0.30

cost = $7.20

Small power ratings can therefore become significant when devices operate for long periods.

---

Power and Current

From:

P = VI

for a fixed voltage:

P ∝ I

A higher-power device generally requires more current when operated at the same voltage.

For example, at 230 V:

230 W appliance

I = 230/230

I = 1 A

2300 W appliance

I = 2300/230

I = 10 A

The higher-power appliance requires much more current.

---

Why Current Matters

Large currents can cause significant heating in wires.

Heating power is:

P = I²R

If current doubles:

I → 2I

then:

P → (2I)²R

P → 4I²R

Therefore:

doubling the current produces four times the heating power

for the same resistance.

This is why high-current circuits require suitable wiring and protection.

---

Electrical Heating

In a resistor:

P = I²R

Electrical energy is transferred mainly into thermal energy.

This is useful in devices such as:

• kettles
• toasters
• electric ovens
• hair dryers
• space heaters

A heating element is designed to transfer electrical energy into thermal energy efficiently for the intended purpose.

---

Power Dissipation in a Resistor

Suppose:

R = 10 Ω

I = 0.5 A

Then:

P = I²R

P = 0.5² × 10

P = 0.25 × 10

P = 2.5 W

If the resistor is rated for only:

0.25 W

it would be unsuitable because the expected power dissipation greatly exceeds its rating.

---

Resistor Power Ratings

Real resistors have maximum power ratings.

Common ratings include:

• 0.125 W
• 0.25 W
• 0.5 W
• 1 W
• 2 W

Higher-power resistors are generally physically larger because they need to transfer thermal energy to their surroundings safely.

Circuit designers should choose a resistor whose power rating safely exceeds the expected operating power.

---

Power in Series Circuits

In a series circuit:

current is the same through each resistor

Since:

P = I²R

a larger resistance dissipates more power when the same current flows through all components.

Suppose:

I = 2 A

R₁ = 2 Ω

R₂ = 5 Ω

Then:

P₁ = 2² × 2

P₁ = 8 W

P₂ = 2² × 5

P₂ = 20 W

The larger resistor transfers energy at a greater rate.

---

Power in Parallel Circuits

In a parallel circuit:

voltage is the same across each branch

Since:

P = V²/R

at the same voltage, a lower resistance dissipates more power.

Suppose:

V = 12 V

R₁ = 6 Ω

R₂ = 12 Ω

Then:

P₁ = 12²/6

P₁ = 24 W

P₂ = 12²/12

P₂ = 12 W

The lower-resistance branch transfers energy at the greater rate.

---

Total Power in a Circuit

The total power supplied by a source equals the total power transferred by the components in an ideal circuit.

P_total = P₁ + P₂ + P₃ + ...

This follows from conservation of energy.

For example:

P₁ = 20 W

P₂ = 30 W

P₃ = 10 W

Then:

P_total = 20 + 30 + 10

P_total = 60 W

The source must supply approximately 60 W.

---

Power Supplied by a Battery

For a battery with emf ε supplying current I:

P_source = εI

If:

ε = 12 V

I = 3 A

then:

P_source = 12 × 3

P_source = 36 W

A real battery may transfer some of this power internally because of internal resistance.

---

Internal Power Loss

For a battery with internal resistance r:

P_internal = I²r

Suppose:

I = 3 A

r = 0.20 Ω

Then:

P_internal = 3² × 0.20

P_internal = 9 × 0.20

P_internal = 1.8 W

This energy is mainly transferred into thermal energy inside the battery.

---

Useful Power from a Real Battery

If the terminal voltage is V:

P_external = VI

The energy balance is:

P_source = P_external + P_internal

or:

εI = VI + I²r

This connects electrical power with conservation of energy.

---

Power and Efficiency

Efficiency can be expressed using power:

efficiency = useful power output / total power input × 100%

Suppose a motor receives:

500 W

and produces:

400 W

of useful mechanical power.

Efficiency:

efficiency = 400/500 × 100%

efficiency = 80%

The remaining:

100 W

is transferred into other forms such as thermal energy and sound.

---

Comparing Two Motors

Motor A:

input power = 600 W

useful output = 450 W

Efficiency:

450/600 × 100%

= 75%

Motor B:

input power = 550 W

useful output = 440 W

Efficiency:

440/550 × 100%

= 80%

Motor B uses less input power and has greater efficiency, although Motor A produces slightly more useful output power.

This shows why several factors should be considered when comparing devices.

---

Power Ratings and Performance

A higher power rating does not necessarily mean that a device is "better."

It means the device transfers energy at a greater rate under its rated conditions.

Whether this is desirable depends on the purpose.

For example:

• a high-power kettle may heat water faster
• a high-power heater may warm a room faster
• a lower-power lamp may produce similar light if it is more efficient
• a lower-power computer may be preferable if it provides sufficient performance

Power should therefore be interpreted in context.

---

Power Ratings and Safety

Power ratings can also help determine electrical safety requirements.

A high-power appliance usually draws a larger current.

For example:

P = 3000 W

V = 230 V

I = P/V

I = 3000/230

I ≈ 13.0 A

Wires, plugs, switches and protective devices must be capable of safely carrying the required current.

---

Appliance Labels

Electrical appliance labels may include:

• rated voltage
• rated current
• rated power
• frequency
• safety information

These values help users determine whether the device is suitable for a particular electrical supply.

---

Worked Multi-Step Problem

A heater has:

R = 46 Ω

and is connected to:

V = 230 V

Calculate current

I = V/R

I = 230/46

I = 5 A

Calculate power

P = VI

P = 230 × 5

P = 1150 W

Alternatively:

P = V²/R

P = 230²/46

P = 1150 W

Energy transferred in 10 minutes

10 min = 600 s

E = Pt

E = 1150 × 600

E = 690,000 J

or:

690 kJ

---

Worked Appliance Cost Problem

A 2.4 kW appliance operates for:

30 minutes per day

for:

20 days

Convert:

30 min = 0.5 h

Daily energy:

E = 2.4 × 0.5

E = 1.2 kWh

Over 20 days:

E = 1.2 × 20

E = 24 kWh

If electricity costs:

$0.28/kWh

cost:

24 × 0.28

= $6.72

---

Choosing the Right Power Equation

A useful strategy is to identify what the question gives you.

If you know:

energy and time → P = E/t

voltage and current → P = VI

current and resistance → P = I²R

voltage and resistance → P = V²/R

Do not calculate unnecessary quantities if a direct equation is available.

---

Unit Conversions

Power calculations often require unit conversions.

Power

1000 W = 1 kW

1 MW = 1,000,000 W

Current

1000 mA = 1 A

Time

60 s = 1 min

3600 s = 1 h

Energy

1 kWh = 3.6 MJ

Always check the required units before substituting into an equation.

---

Example with Milliamps

An electronic component operates at:

V = 12 V

I = 250 mA

Convert:

250 mA = 0.250 A

Then:

P = VI

P = 12 × 0.250

P = 3.0 W

Failing to convert mA to A would produce an answer 1000 times too large.

---

Power and Conservation of Energy

Electrical power is ultimately about the rate of energy transfer.

For a circuit:

power supplied = total rate of energy transfer

In an ideal model:

P_source = ΣP_components

In a real system, all energy transfers must still be included.

Some may be:

• useful mechanical power
• useful light
• useful heating
• unwanted heating
• sound

Energy is conserved even when a device is inefficient.

---

Common Mistakes

Mistake: Confusing power with energy.
Power is the rate of energy transfer; energy is the total amount transferred.

Mistake: Saying watts measure energy.
Watts measure power. Joules and kilowatt-hours measure energy.

Mistake: Forgetting to square current in P = I²R.
The equation contains I², not I.

Mistake: Forgetting to square voltage in P = V²/R.

Mistake: Using milliamps as though they were amperes.
Convert mA to A.

Mistake: Assuming the highest-power appliance always uses the most energy.
Operating time matters.

Mistake: Assuming a higher power rating always means greater efficiency.
Power and efficiency are different quantities.

Mistake: Ignoring component power ratings.
A resistor may have the correct resistance but still be unable to safely dissipate the required power.

Mistake: Mixing watts and kilowatts in kWh calculations.
Use power in kilowatts when calculating kWh.

---

Key Terms

Electrical power — rate at which electrical energy is transferred.

Power — energy transferred per unit time.

Watt (W) — SI unit of power; one joule per second.

Kilowatt (kW) — 1000 watts.

Power rating — power a device is designed to transfer under specified operating conditions.

Power dissipation — rate at which electrical energy is transferred by a component, often as thermal energy.

Joule heating — transfer of electrical energy into thermal energy due to resistance.

Energy consumption — total amount of electrical energy used or transferred over time.

Kilowatt-hour (kWh) — unit of energy equal to 3.6 MJ.

Efficiency — proportion of input power or energy transferred usefully.

Rated voltage — voltage at which a device is designed to operate.

Rated current — current expected under specified operating conditions.

Power loss — power transferred in an unwanted form, commonly thermal energy.

---

Key Takeaways

• Electrical power is the rate at which electrical energy is transferred.
• The SI unit of power is the watt.
• 1 W = 1 J/s.
• The basic power equation is P = E/t.
• Electrical power can be calculated using P = VI.
• For resistors, power can also be calculated using P = I²R and P = V²/R.
• The appropriate equation depends on the quantities provided.
• Power ratings describe the rate of energy transfer under specified operating conditions.
• Higher power means faster energy transfer, not necessarily greater total energy consumption.
• Total energy depends on both power and operating time.
• E = Pt.
• Appliance energy consumption is commonly measured in kWh.
• 1 kWh = 3.6 MJ.
• High-power devices generally draw larger currents when operating at the same voltage.
• Heating in resistive components follows P = I²R.
• Doubling current produces four times the resistive heating for the same resistance.
• Components must have suitable power ratings.
• Total circuit power is the sum of the power transferred by its components.
• Real batteries can lose power internally through their internal resistance.
• Efficiency compares useful output power with total input power.
• Appliance comparisons should consider power, operating time, energy consumption, efficiency and useful performance.

Check Your Understanding

1. Define electrical power.
2. What is the SI unit of power?
3. What does a power of 1 W mean?
4. Explain the difference between electrical power and electrical energy.
5. A device transfers 12,000 J in 60 s. Calculate its power.
6. A device operates at 12 V and draws 3 A. Calculate its power.
7. A 230 V appliance is rated at 1840 W. Calculate its current.
8. A 5 Ω resistor carries 4 A. Calculate its power using P = I²R.
9. A 20 Ω resistor has 10 V across it. Calculate its power using P = V²/R.
10. Derive P = I²R from P = VI and Ohm's Law.
11. Derive P = V²/R from P = VI and Ohm's Law.
12. Explain what a 2000 W rating on a heater means.
13. A 2 kW heater operates for 2.5 hours. Calculate the energy consumed in kWh.
14. Convert the answer to Question 13 into joules.
15. A 100 W television operates for 6 hours while a 2000 W kettle operates for 6 minutes. Which device transfers more energy?
16. Explain why doubling current through a resistor causes four times the heating power.
17. A motor receives 800 W and provides 680 W of useful mechanical power. Calculate its efficiency.
18. Explain why a higher-power appliance is not necessarily more energy efficient.
19. A 0.25 W resistor is expected to dissipate 1.5 W. Explain why this is a problem and how the design could be improved.
20. Explain how power rating, operating time, efficiency and energy consumption should all be considered when comparing electrical appliances.

Household Electricity

Household Electrical Systems

A household electrical system distributes electrical energy from the electricity supply to appliances, lighting, outlets, and other devices throughout a building.

Most household systems contain:

• an incoming electricity supply
• an electricity meter
• a distribution board or consumer unit
• circuit breakers or fuses
• electrical wiring
• switches
• outlets
• appliances
• protective earthing or grounding systems

Different countries use different supply voltages, frequencies, plugs, and wiring standards, but the underlying electrical principles are similar.

---

From the Power Grid to the Home

Electrical energy is generated and distributed through an electrical grid.

Electricity is transmitted over long distances at high voltages because this reduces energy losses in transmission lines.

Transformers reduce the voltage before electricity reaches homes and other buildings.

A simplified sequence is:

power station → transmission network → substations → distribution network → household

The household electrical system then distributes the supply among different circuits.

---

Alternating Current

Household electricity is normally supplied as alternating current (AC).

In alternating current:

the direction of current repeatedly reverses

and the voltage also changes direction periodically.

This differs from direct current (DC), where charge flows in one overall direction.

---

AC and DC

Alternating Current — AC

In AC:

• current repeatedly reverses direction
• voltage polarity repeatedly reverses
• household mains electricity is normally AC
• transformers can conveniently change AC voltage levels

Direct Current — DC

In DC:

• current has one overall direction
• polarity normally remains fixed
• batteries supply DC
• many electronic devices operate internally using DC

---

Comparing AC and DC

Many household devices receive AC from an outlet but convert it to DC internally.

---

AC Frequency

AC changes direction periodically.

The number of complete cycles per second is called the frequency.

Frequency is measured in:

hertz (Hz)

For example:

50 Hz means:

50 complete AC cycles occur each second

Different electrical systems around the world use different standard mains frequencies.

---

Household Supply Voltage

Household mains voltage varies by country.

Many countries use nominal supplies around:

220–240 V AC

while others commonly use supplies around:

100–127 V AC

Always use the locally specified voltage and electrical standards rather than assuming that every country uses the same system.

---

Why Household Circuits Use Parallel Connections

Household appliances are generally connected in parallel rather than in one long series circuit.

This has several advantages.

Each appliance receives approximately the supply voltage.

Each appliance can also be switched independently.

If one appliance is turned off or fails, other branches can continue operating.

---

Current in Household Circuits

The current drawn by an appliance depends on its power and operating voltage.

Since:

P = VI

we can calculate:

I = P/V

A higher-power appliance generally draws a larger current when connected to the same supply voltage.

---

Appliance Current Example

Suppose a kettle is rated:

230 V

2300 W

Current:

I = P/V

I = 2300/230

I = 10 A

A 230 W appliance connected to the same voltage would draw:

I = 230/230

I = 1 A

The kettle therefore requires ten times the current.

---

Electrical Power in the Home

Electrical appliances have different power requirements.

Typical categories include:

Low-power devices

• LED lighting
• phone chargers
• small electronics

Medium-power devices

• televisions
• computers
• fans
• refrigerators during operation

High-power devices

• kettles
• ovens
• heaters
• hair dryers
• air conditioners
• water heaters

Actual power ratings vary substantially between models, so appliance labels should be checked.

---

Appliance Ratings

Electrical appliances usually have a rating label or nameplate.

It may show:

• voltage
• frequency
• power
• current
• model information
• safety certification
• insulation information

For example:

230 V

50 Hz

1500 W

This indicates the electrical conditions for which the appliance was designed.

---

Interpreting an Appliance Rating

Suppose an appliance is labelled:

230 V

50 Hz

1150 W

The rated current is approximately:

I = P/V

I = 1150/230

I = 5 A

This information helps determine whether the:

• supply is appropriate
• wiring is suitable
• plug is suitable
• protective device is suitable

---

Why Voltage Ratings Matter

An appliance should be operated using an appropriate supply voltage.

If the applied voltage is much too high, it may cause:

• excessive current
• overheating
• insulation damage
• component failure

If the voltage is too low, the appliance may:

• operate weakly
• fail to start
• perform incorrectly
• draw unexpected currents depending on its design

---

Why Frequency Ratings Matter

Some appliances are also designed for a particular AC frequency.

For example, a label may state:

50–60 Hz

This means the device is designed to operate across that frequency range.

Frequency can be particularly important for equipment containing:

• motors
• transformers
• timing systems

---

Household Wiring

Household wiring must provide safe conducting paths for current.

Common systems include conductors serving functions such as:

• live or line
• neutral
• protective earth or ground

The exact wire colors and arrangements depend on local electrical standards.

Never assume wire function from color alone when dealing with unfamiliar or real installations.

---

Live or Line Conductor

The live, or line, conductor carries the alternating voltage from the supply toward the appliance.

It can have a dangerous potential relative to earth.

Contact with an energized live conductor can cause a severe electric shock.

---

Neutral Conductor

The neutral conductor normally provides a return path for current.

It is maintained close to earth potential within the supply system, although it should never be treated casually as a guaranteed safe conductor.

Electrical installations should always be treated according to appropriate safety procedures.

---

Protective Earth or Ground

The protective earth conductor provides an important safety path.

If a fault causes a live conductor to contact an exposed conductive case, the protective earth can provide a low-resistance fault-current path.

This helps protective devices disconnect the faulty circuit rapidly.

---

Why Earthing Improves Safety

Consider an appliance with a metal case.

Normally:

the metal case should not be live

Suppose damaged insulation causes the live conductor to contact the case.

Without suitable protection, someone touching the case could potentially become part of the current path.

With effective protective earthing, a large fault current can flow through the protective path.

This can cause the circuit's protective device to disconnect the supply.

---

Double Insulation

Some appliances do not require a protective earth connection because they use double insulation.

Double-insulated appliances are designed with additional insulating barriers so that accessible parts are separated from dangerous electrical conductors.

A common symbol consists of:

a square inside another square

Double insulation is common in some appliances with non-conductive outer cases.

---

Electrical Safety Devices

Household electrical systems use several types of protection.

These may include:

• fuses
• circuit breakers
• residual-current protection
• protective earthing
• insulation
• correctly rated wiring

No single safety device protects against every possible electrical hazard.

---

Fuses

A fuse contains a conductor designed to melt when excessive current flows.

When the fuse melts:

the circuit opens

and current stops.

This can help prevent:

• overheating
• wire damage
• equipment damage
• fire

A blown fuse must be replaced with an appropriate type and rating after the cause of the fault has been identified.

---

Circuit Breakers

A circuit breaker automatically opens a circuit when certain dangerous conditions occur.

Depending on the type, circuit breakers can respond to:

• overloads
• short circuits

Unlike a traditional fuse, many circuit breakers can be reset after the fault has been corrected.

---

Fuse vs Circuit Breaker

Both are intended to interrupt dangerous currents.

---

Residual-Current Protection

A residual-current device (RCD) or similar ground-fault protection device compares currents in the supply conductors.

Under normal conditions:

current leaving through the live conductor ≈ current returning through the neutral conductor

If some current takes an unintended path, such as through earth, an imbalance appears.

The device can rapidly disconnect the circuit.

Terminology and specific devices differ between electrical systems.

---

Example of Residual-Current Protection

Suppose:

5.00 A

flows out through the live conductor.

Only:

4.97 A

returns through neutral.

Difference:

5.00 − 4.97

= 0.03 A

or:

30 mA

The missing current is flowing through another path.

A suitable protective device may detect this imbalance and disconnect the supply.

---

Overloads

An overload occurs when a circuit carries more current than it is designed to carry for a sustained period.

For example, connecting too many high-power appliances to one circuit can create excessive current.

Since:

P = VI

at approximately constant supply voltage:

greater total power → greater total current

---

Overload Example

Suppose three appliances operate from the same 230 V circuit:

heater = 2000 W

kettle = 2300 W

hair dryer = 1800 W

Total power:

P_total = 2000 + 2300 + 1800

P_total = 6100 W

Approximate current:

I = P/V

I = 6100/230

I ≈ 26.5 A

Whether this is acceptable depends on the rating of the actual circuit and its protective devices.

---

Why Excessive Current Is Dangerous

Wires have resistance.

Heating power is:

P = I²R

This means current has a particularly strong effect on heating.

If current doubles:

P_new = (2I)²R

P_new = 4I²R

Therefore:

doubling current produces four times the resistive heating

for the same resistance.

Excessive current can cause insulation and wiring to overheat.

---

Short Circuits

A short circuit occurs when an unintended very low-resistance path forms.

Using:

I = V/R

if resistance becomes very small, current can become very large.

This can cause:

• rapid heating
• damaged conductors
• damaged power sources
• sparks or arcing
• fire risk

Fuses and circuit breakers are designed to interrupt dangerous fault currents.

---

Electric Shock

An electric shock occurs when current passes through the body.

The effect depends on factors including:

• current magnitude
• path through the body
• duration
• frequency
• skin condition
• contact area

Mains electricity can cause serious injury or death.

Household electrical equipment should therefore never be treated as a safe classroom circuit.

---

Water and Electricity

Water can greatly increase electrical danger, particularly when dissolved ions make it conductive and when wet skin reduces electrical resistance.

This is why extra precautions are important around:

• bathrooms
• kitchens
• outdoor electrical equipment
• pools
• wet floors

Never handle mains electrical equipment with wet hands.

---

Damaged Cables

A damaged cable may expose conductive wires.

Possible hazards include:

• electric shock
• short circuits
• arcing
• overheating
• fire

Damaged mains cables should not simply be covered casually and continued in service. Appropriate repair or replacement is required.

---

Overloaded Outlets and Power Strips

Power strips do not create additional electrical capacity.

Connecting many high-power devices to one outlet or circuit can produce excessive current.

For example, several:

• heaters
• kettles
• cooking appliances
• hair dryers

on the same circuit can create a significant load.

The total expected power and current should remain within the ratings of the equipment and electrical circuit.

---

Extension Leads

Extension leads can become hazardous if they are:

• overloaded
• damaged
• poorly connected
• used in unsuitable environments
• operated while tightly coiled under substantial load

Current flowing through resistance produces heat.

Good electrical practice requires using equipment within its specified ratings.

---

Loose Connections

A loose electrical connection can have greater resistance than a secure connection.

Since:

P = I²R

a high-resistance connection carrying substantial current can become hot.

This can cause:

• local overheating
• damaged insulation
• arcing
• equipment failure

Good mechanical and electrical connections are therefore important for safety.

---

Switches

A switch opens or closes a circuit.

Closed switch

Provides a conducting path.

Open switch

Interrupts the conducting path.

In appropriate mains wiring systems, switches are arranged so that equipment is safely disconnected from the energized conductor when switched off.

The exact wiring requirements are determined by local electrical codes.

---

Appliance Power and Energy Consumption

Power tells us how quickly an appliance transfers energy.

Energy is:

E = Pt

A high-power appliance may use a large amount of energy quickly.

However, operating time is also important.

---

Example: Kettle

A kettle has:

P = 2000 W

and operates for:

3 minutes

Convert time:

3 min = 180 s

Energy:

E = Pt

E = 2000 × 180

E = 360,000 J

or:

360 kJ

---

Example: Television

A television has:

P = 100 W

and operates for:

4 hours

Energy in kWh:

100 W = 0.100 kW

E = 0.100 × 4

E = 0.40 kWh

The total energy consumed depends on both power and time.

---

Kilowatt-Hours

Household electrical energy is commonly measured in:

kilowatt-hours (kWh)

Use:

E = Pt

with:

P in kW

and:

t in hours

For example:

2 kW × 3 h = 6 kWh

Remember:

1 kWh = 3.6 MJ

A kilowatt-hour is a unit of energy, not power.

---

Electricity Meters

An electricity meter measures the electrical energy supplied to a household.

Modern systems may use electronic or smart meters.

Energy consumption is typically recorded in kilowatt-hours.

This information can be used for:

• billing
• monitoring consumption
• identifying high-energy periods
• improving energy efficiency

---

Calculating Electricity Cost

Suppose an appliance uses:

3 kWh

and electricity costs:

$0.30/kWh

Cost:

cost = energy × price

cost = 3 × 0.30

cost = $0.90

Actual tariffs may include other charges, but this calculation gives the energy-related cost.

---

Comparing Household Appliances

Suppose two devices perform similar functions.

Device A

Power = 1500 W

Operating time = 1 h

Energy:

1.5 kWh

Device B

Power = 1000 W

Operating time = 1.5 h

Energy:

1.5 kWh

Although Device B has lower power, both use the same total energy in this example.

Power alone does not determine energy consumption.

---

Energy Efficiency

Electrical devices often transform electrical energy into several forms.

For example, a motor may produce:

• useful kinetic energy
• thermal energy
• sound

Efficiency is:

efficiency = useful energy output / total energy input × 100%

or:

efficiency = useful power output / total power input × 100%

More efficient devices provide a greater useful output for a given input.

---

Household Lighting

Lighting provides a good example of differences in electrical efficiency.

Different lamp technologies can produce similar useful illumination while requiring different amounts of electrical power.

More efficient lighting can therefore reduce:

• energy consumption
• unwanted heating
• operating cost

---

Standby Power

Some appliances consume electrical power even when they appear to be off or inactive.

Examples may include:

• televisions
• computers
• chargers
• network equipment
• smart appliances

A small standby power operating continuously can add up over long periods.

---

Example: Standby Energy

Suppose a device draws:

5 W

for:

24 h

Convert:

5 W = 0.005 kW

Energy:

E = 0.005 × 24

E = 0.12 kWh per day

Over 30 days:

E = 0.12 × 30

E = 3.6 kWh

This illustrates how low power used continuously can become significant.

---

Household Electrical Hazards

Common hazards include:

• damaged insulation
• exposed conductors
• overloaded circuits
• damaged plugs
• wet electrical equipment
• loose connections
• unsuitable extension leads
• incorrect fuses
• short circuits
• poorly maintained appliances
• unauthorized modifications

Electrical safety depends on both good system design and responsible use.

---

Safe Behavior Around Household Electricity

Important precautions include:

• keep electrical equipment away from water
• do not use damaged cords
• avoid overloaded outlets
• use correctly rated equipment
• disconnect equipment appropriately before servicing
• never insert objects into electrical outlets
• do not bypass safety devices
• use qualified professionals for mains electrical work

Household mains electricity is fundamentally different from low-voltage classroom circuit experiments.

---

Reading an Appliance Label

Suppose an appliance label states:

220–240 V AC

50–60 Hz

1200 W

This tells us that:

• the appliance requires AC
• it is designed for supplies in the stated voltage range
• it can operate across the stated frequency range
• its rated power is approximately 1200 W under specified operating conditions

At 240 V:

I = P/V

I = 1200/240

I = 5.0 A

At 220 V, the actual behavior depends on the device design; P = VI can be used when the relevant operating power/current values are known.

---

Appliance Compatibility

Before connecting an appliance to an unfamiliar electricity supply, check:

• voltage
• AC/DC requirement
• frequency
• plug and connector compatibility
• power requirements

A plug adapter changes the physical connection.

It does not necessarily change the voltage or frequency.

This distinction is especially important when electrical devices are used internationally.

---

AC Adapters and Chargers

Many electronic devices require low-voltage DC internally.

A charger or power adapter may accept:

100–240 V AC, 50–60 Hz

and produce something such as:

5 V DC

The adapter therefore changes the electrical supply into a form suitable for the device.

Always check the actual input and output ratings rather than assuming compatibility.

---

Interpreting Charger Ratings

Suppose a charger states:

Input:

100–240 V AC
50–60 Hz

Output:

5 V DC
3 A

Maximum output power at that output condition is:

P = VI

P = 5 × 3

P = 15 W

The input and output ratings describe different sides of the power conversion system.

---

Household Circuit Troubleshooting

Warning signs of electrical problems can include:

• repeated breaker trips
• repeated blown fuses
• burning smells
• discolored outlets
• unusual heating
• sparks
• buzzing or crackling
• damaged cables

These should not simply be ignored or repeatedly reset without investigating the cause.

For mains electrical systems, potentially dangerous faults should be handled by appropriately qualified personnel.

---

Common Mistakes

Mistake: Saying AC travels one way and then stops.
AC repeatedly reverses direction.

Mistake: Saying batteries normally provide AC.
Batteries provide DC.

Mistake: Assuming every country uses the same mains voltage and frequency.
Electrical standards vary.

Mistake: Saying household appliances are connected in series.
Household loads are generally connected in parallel.

Mistake: Thinking a fuse supplies electricity.
A fuse is a protection device.

Mistake: Assuming a circuit breaker and residual-current device detect exactly the same fault.
They are designed for different types of protection.

Mistake: Assuming neutral should always be treated as harmless.
Electrical conductors should be handled according to proper safety procedures.

Mistake: Assuming a plug adapter changes voltage.
Many adapters only change the physical connector.

Mistake: Confusing kW with kWh.
kW measures power; kWh measures energy.

Mistake: Assuming lower power always means lower total energy consumption.
Operating time also matters.

---

Key Terms

Household electricity — electrical energy supplied and distributed within a home.

Alternating current (AC) — current whose direction periodically reverses.

Direct current (DC) — current with one overall direction.

Frequency — number of complete cycles per second, measured in hertz.

Hertz (Hz) — unit of frequency; one cycle per second.

Live/line conductor — conductor carrying the energized supply voltage.

Neutral conductor — conductor that normally provides a return path and is maintained near earth potential within the supply system.

Protective earth/ground — safety conductor providing a fault-current path.

Fuse — device designed to open a circuit when excessive current causes its fuse element to melt.

Circuit breaker — resettable protective device that automatically interrupts certain excessive currents.

Residual-current device (RCD) — protective device that detects an imbalance between outgoing and returning current.

Overload — condition in which excessive current is drawn for a circuit's intended rating.

Short circuit — unintended low-resistance current path.

Double insulation — construction using additional insulation barriers to protect users from dangerous voltages.

Power rating — rate of energy transfer for which a device is designed under specified conditions.

Kilowatt-hour (kWh) — unit of electrical energy equal to 3.6 MJ.

Appliance rating — electrical operating information provided by the manufacturer.

---

Key Takeaways

• Household electrical systems distribute electrical energy safely to multiple loads.
• Household mains electricity is normally AC.
• Batteries normally provide DC.
• AC repeatedly reverses direction and has a frequency.
• Household supply voltage and frequency vary between countries.
• Household loads are generally connected in parallel.
• Parallel connections allow devices to receive the supply voltage and operate independently.
• Electrical power is calculated using P = VI.
• Higher-power appliances generally draw more current at the same voltage.
• Excessive current can cause dangerous heating because P = I²R.
• Fuses and circuit breakers protect against excessive current.
• Residual-current protection detects certain unintended current paths.
• Protective earthing can help make exposed conductive cases safer during faults.
• Double insulation provides another form of protection in suitable appliances.
• Water, damaged insulation, overloaded circuits and loose connections can create serious hazards.
• Appliance ratings provide information about voltage, frequency, power and sometimes current.
• A plug adapter does not necessarily convert voltage.
• Household energy consumption is commonly measured in kWh.
• Power and energy are different: energy consumption depends on both power and operating time.
• Electrical safety devices reduce risk, but safe behavior and correct installation remain essential.

Check Your Understanding

1. Describe the basic purpose of a household electrical system.
2. Explain the difference between AC and DC.
3. Which type of current is normally supplied by a battery?
4. Which type of current is normally used for household mains electricity?
5. What does a frequency of 50 Hz mean?
6. Why are household appliances generally connected in parallel rather than series?
7. A 2300 W appliance operates at 230 V. Calculate its current.
8. Explain the purpose of a fuse.
9. Explain the purpose of a circuit breaker.
10. How does residual-current protection differ from ordinary overcurrent protection?
11. Explain how protective earthing can reduce danger if a live conductor contacts a metal appliance case.
12. What is meant by double insulation?
13. Explain why excessive current can cause electrical wiring to overheat.
14. Three appliances connected to the same 230 V circuit have powers of 1200 W, 1800 W and 2300 W. Calculate their total current if they operate simultaneously.
15. Identify four common household electrical hazards.
16. An appliance is labelled 230 V, 50 Hz, 920 W. Calculate its rated current.
17. Explain the difference between kW and kWh.
18. A 1.5 kW appliance operates for 4 hours. Calculate its energy consumption in kWh.
19. Explain why a physical plug adapter does not necessarily make an appliance electrically compatible with another country's supply.
20. Describe how appliance ratings, circuit protection and safe electrical practices work together to reduce risks in household electrical systems.

Efficiency and Energy Use

What Is Efficiency?

Efficiency describes how much of the energy supplied to a device is transferred in a useful way.

No real electrical device transfers all of its input energy into the desired output. Some energy is usually transferred to the surroundings in unwanted forms, often as thermal energy or sound.

Efficiency can be calculated using:

efficiency = useful energy output / total energy input

As a percentage:

efficiency = useful energy output / total energy input × 100%

Efficiency can also be calculated using power:

efficiency = useful power output / total power input × 100%

---

Understanding Efficiency

Suppose an electrical device receives:

100 J

of energy.

If:

80 J

is transferred usefully, its efficiency is:

efficiency = 80/100 × 100%

efficiency = 80%

The remaining:

100 − 80 = 20 J

is transferred in other ways.

The energy has not disappeared.

---

Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed.

Therefore:

total energy input = total energy output

For a device:

input energy = useful energy output + unwanted energy transfers

For example:

500 J input = 400 J useful + 100 J unwanted

Energy is conserved even if the device is inefficient.

---

Energy Losses

We often describe unwanted energy transfers as energy losses.

However, the energy is not actually destroyed.

It has usually been transferred to the surroundings in forms that are less useful for the intended purpose.

Common unwanted transfers include:

• thermal energy
• sound
• vibration
• frictional heating
• electrical resistance

---

Example: Electric Motor

An electric motor receives:

1000 J

of electrical energy.

It produces:

850 J

of useful mechanical energy.

The remaining energy is:

1000 − 850

= 150 J

This may be transferred as:

• thermal energy
• sound
• vibration

Efficiency:

850/1000 × 100%

= 85%

---

Efficiency Using Power

Because power is the rate of energy transfer, efficiency can also be calculated using:

efficiency = useful power output / input power × 100%

Suppose a motor receives:

P_input = 800 W

and produces:

P_useful = 680 W

Then:

efficiency = 680/800 × 100%

efficiency = 85%

The unwanted power transfer is:

800 − 680

= 120 W

---

Calculating Useful Energy

The efficiency equation can be rearranged.

Using efficiency as a decimal:

useful energy = efficiency × input energy

Suppose:

input energy = 2000 J

efficiency = 75%

Convert:

75% = 0.75

Then:

useful energy = 0.75 × 2000

useful energy = 1500 J

---

Calculating Input Energy

The equation can also be rearranged:

input energy = useful energy / efficiency

Suppose a machine must provide:

900 J

of useful energy and is:

60% efficient.

Convert:

60% = 0.60

Then:

input energy = 900/0.60

input energy = 1500 J

The unwanted transfer is:

1500 − 900

= 600 J

---

Efficiency Cannot Normally Exceed 100%

Efficiency cannot normally be greater than:

100%

A claimed efficiency of 120%, for example, would mean the useful energy output is greater than the total energy input being counted.

That would violate conservation of energy if all relevant energy inputs and outputs were properly included.

An answer above 100% usually indicates:

• calculation error
• incorrect measurements
• missing energy input
• incorrect interpretation of the system

---

Useful Energy Depends on Purpose

Whether an energy transfer is useful depends on what the device is designed to do.

Electric heater

Useful output:

thermal energy

Electric motor

Useful output:

mechanical energy

Lamp

Useful output:

light

Speaker

Useful output:

sound

Thermal energy from a heater is useful.

Thermal energy from a motor is usually unwanted.

---

Energy Flow

Consider a lamp receiving:

100 J

of electrical energy.

Suppose:

25 J → useful light

75 J → thermal energy

Efficiency:

25/100 × 100%

= 25%

Energy conservation:

100 J = 25 J + 75 J

The lamp does not lose 75 J from existence. That energy is transferred into the surroundings.

---

Sankey Diagrams

A Sankey diagram represents energy transfers using arrows.

The width of each arrow represents the amount of energy transferred.

For example:

100 J input

→ 80 J useful output

→ 20 J unwanted output

A more efficient device has a greater proportion of its input arrow continuing into the useful output.

---

Electrical Resistance and Energy Loss

When current flows through resistance, electrical energy is transferred into thermal energy.

The heating power is:

P = I²R

Therefore, unwanted heating increases with:

• greater resistance
• greater current

Because current is squared, increasing current can dramatically increase heating losses.

---

Effect of Current on Energy Loss

Suppose a wire has:

R = 2 Ω

and carries:

I = 3 A

Heating power:

P = I²R

P = 3² × 2

P = 18 W

If current doubles to:

6 A

then:

P = 6² × 2

P = 72 W

Doubling the current produces:

four times the heating power

---

Reducing Electrical Transmission Losses

Electrical power transmission provides an important application of efficiency.

Power transmitted is approximately:

P = VI

For the same transmitted power, increasing voltage allows the current to decrease.

Heating losses in transmission wires are:

P_loss = I²R

Therefore:

higher transmission voltage → lower current → lower I²R losses

This is one major reason electricity is transmitted at very high voltages.

---

Example: Transmission Loss

Suppose a transmission line has:

R = 5 Ω

and carries:

I = 100 A

Power lost:

P_loss = I²R

P_loss = 100² × 5

P_loss = 50,000 W

or:

50 kW

If the current were reduced to:

20 A

then:

P_loss = 20² × 5

P_loss = 2000 W

or:

2 kW

The current has fallen by a factor of 5, but the heating loss has fallen by a factor of 25.

---

Comparing Efficient Technologies

Two devices designed for the same purpose may use very different amounts of electrical energy.

A fair comparison should consider:

• useful output
• input power
• operating time
• efficiency
• energy consumption
• expected lifetime
• required performance

Simply choosing the device with the lowest power rating does not always produce the best comparison.

---

Efficient Lighting

Lighting is a useful example.

An inefficient lamp may transfer a large proportion of its electrical input into unwanted thermal energy.

A more efficient lamp produces the required illumination while using less electrical power.

Modern LED lighting can provide high luminous output while requiring much less electrical power than many older lighting technologies.

---

Comparing Two Lamps

Suppose two lamps provide similar useful illumination.

Lamp A:

P = 60 W

Lamp B:

P = 10 W

Both operate for:

5 h

Lamp A

60 W = 0.060 kW

E = Pt

E = 0.060 × 5

E = 0.30 kWh

Lamp B

10 W = 0.010 kW

E = 0.010 × 5

E = 0.05 kWh

For the same operating time:

Lamp B uses:

0.25 kWh less energy

---

Percentage Energy Saving

Energy saving can be expressed as a percentage.

percentage saving = (original use − new use) / original use × 100%

Using the previous lamps:

percentage saving = (0.30 − 0.05)/0.30 × 100%

percentage saving ≈ 83.3%

This comparison assumes the lamps provide a sufficiently similar useful lighting output.

---

Efficient Motors

Electric motors are used in:

• fans
• pumps
• refrigerators
• air-conditioning systems
• elevators
• industrial machinery
• electric vehicles

Improving motor efficiency can reduce energy consumption significantly because many motors operate for long periods.

Efficiency can be improved through:

• lower electrical resistance
• reduced friction
• improved magnetic design
• appropriate motor sizing
• efficient control systems

---

Heating Devices and Efficiency

Electrical resistance heaters can convert a very large proportion of their electrical input into thermal energy at the point of use.

If the goal is simply to produce heat, that thermal output is useful.

However, this does not automatically mean every electric heating system is the most energy-efficient way to heat a building.

The performance of the entire system must be considered.

---

Heat Pumps

A heat pump uses electrical energy to move thermal energy from one place to another.

Examples include:

• refrigerators
• air conditioners
• heat-pump heating systems

Instead of producing all the thermal energy directly from electrical resistance, a heat pump transfers thermal energy between environments.

For heat pumps, engineers often use a measure called coefficient of performance (COP) rather than ordinary energy-conversion efficiency.

This distinction is important because a heat pump can deliver more thermal energy to a room than the electrical energy it consumes by transferring additional energy from the environment.

This does not violate conservation of energy.

---

Electrical Energy Consumption

Energy consumption depends on both power and time.

E = Pt

For household electricity:

• P is often measured in kW
• t is measured in hours
• E is measured in kWh

For example:

P = 2 kW

t = 3 h

E = 2 × 3

E = 6 kWh

---

Evaluating Energy Consumption

When evaluating an appliance, ask:

• What is its power?
• How long does it operate?
• How often is it used?
• What useful output does it provide?
• How efficient is it?
• Does it consume standby power?
• Is there a more efficient alternative?

A high-power appliance used briefly may consume less energy than a low-power appliance operating continuously.

---

Example: Kettle vs Television

Kettle

P = 2.0 kW

t = 6 minutes = 0.10 h

E = 2.0 × 0.10

E = 0.20 kWh

Television

P = 0.10 kW

t = 5 h

E = 0.10 × 5

E = 0.50 kWh

The television has much lower power but consumes more energy in this example because it operates much longer.

---

Daily Energy Consumption

Suppose a device has:

P = 500 W = 0.50 kW

and operates for:

6 h/day

Daily energy:

E = 0.50 × 6

E = 3 kWh/day

For 30 days:

E = 3 × 30

E = 90 kWh

Long operating times can make even moderate-power devices significant energy consumers.

---

Calculating Energy Cost

If electricity costs:

$0.30/kWh

and a device uses:

90 kWh

then:

cost = 90 × 0.30

cost = $27

Reducing energy consumption can therefore reduce both:

• energy demand
• operating cost

---

Comparing Two Appliances

Suppose two appliances perform the same task.

Appliance A

Power = 1200 W

Operating time = 2 h

Appliance B

Power = 800 W

Operating time = 2.5 h

Appliance A:

E = 1.2 × 2

E = 2.4 kWh

Appliance B:

E = 0.8 × 2.5

E = 2.0 kWh

Appliance B has the lower total energy consumption even though it operates longer.

---

Standby Power

Some devices consume power while waiting for use.

Examples can include:

• televisions
• game consoles
• computers
• printers
• chargers
• network equipment
• smart appliances

Suppose ten devices each average:

3 W

of unnecessary standby power.

Total:

P = 10 × 3

P = 30 W

Over 24 hours:

E = 0.030 × 24

E = 0.72 kWh/day

Over 365 days:

E = 0.72 × 365

E ≈ 263 kWh

Small continuous loads can become significant over time.

---

Energy-Efficient Appliances

Many modern appliances are designed to reduce energy consumption.

Examples include:

• LED lighting
• efficient refrigerators
• high-efficiency motors
• heat pumps
• variable-speed air conditioners
• efficient power supplies
• smart controls

When comparing devices, energy labels can help estimate their expected consumption under standardized conditions.

---

Energy Labels

Energy labels may provide information such as:

• efficiency rating
• estimated annual energy consumption
• power consumption
• capacity
• performance

However, actual energy use depends on how the device is used.

A highly efficient appliance that operates unnecessarily for long periods can still consume substantial energy.

---

Energy Conservation

Energy conservation in everyday language can mean reducing unnecessary energy consumption.

This is different from the law of conservation of energy.

Law of conservation of energy

Energy cannot be created or destroyed.

Conserving energy

Reducing unnecessary energy consumption or unwanted energy transfers.

The two ideas are related but should not be confused.

---

Reducing Lighting Energy Use

Lighting energy consumption can be reduced by:

• using efficient lamps
• switching lights off when unnecessary
• using daylight where practical
• using occupancy sensors
• using appropriate lighting levels

Both technology and user behavior affect consumption.

---

Reducing Heating and Cooling Energy

Heating and cooling can require large amounts of energy.

Consumption can be reduced through:

• insulation
• reducing unwanted air leakage
• appropriate thermostat settings
• efficient heating/cooling equipment
• shading
• efficient windows
• regular maintenance

Good insulation reduces unwanted thermal energy transfer between the building and its surroundings.

---

Building Insulation

Buildings lose or gain thermal energy through:

• walls
• roofs
• windows
• floors
• air leakage

Improved insulation reduces the rate of unwanted thermal energy transfer.

This reduces the energy required to maintain a comfortable indoor temperature.

---

Reducing Appliance Energy Use

Useful strategies include:

• switching off unnecessary devices
• avoiding unnecessary standby operation
• selecting efficient appliances
• using appropriate operating modes
• maintaining equipment
• using timers or automatic controls
• operating appliances efficiently

The best strategy depends on the device.

---

Efficient Refrigeration

Refrigerators transfer thermal energy from inside the refrigerator to the surrounding room.

Energy consumption can be reduced by:

• good insulation
• effective door seals
• minimizing unnecessary door opening
• appropriate temperature settings
• keeping heat-transfer surfaces functioning properly
• using efficient compressors

A damaged door seal increases thermal energy entering the refrigerator, causing the cooling system to operate more.

---

Efficient Air Conditioning

Air-conditioning systems can be major electrical loads.

Efficiency can be improved through:

• suitable temperature settings
• clean filters
• effective building insulation
• closing doors and windows
• shading from direct sunlight
• efficient variable-speed systems
• appropriate equipment sizing

Reducing the cooling load can be just as important as improving the air conditioner's efficiency.

---

Efficiency and Device Lifetime

Energy efficiency is not the only factor when evaluating technology.

Other considerations include:

• purchase cost
• operating cost
• durability
• maintenance
• useful performance
• materials
• environmental impact
• expected lifetime

A good evaluation considers several factors rather than focusing on a single number.

---

Energy Payback

Some energy-efficient technologies require more energy or resources to manufacture but reduce energy consumption during use.

A complete evaluation can therefore consider:

energy used during manufacture + energy used during operation + energy involved at end of life

This is part of a broader life-cycle analysis.

---

Improving an Inefficient System

Suppose a motor system has:

input power = 1000 W

useful output power = 700 W

Efficiency:

700/1000 × 100%

= 70%

An improved motor produces the same:

700 W

useful output at:

800 W input.

New efficiency:

700/800 × 100%

= 87.5%

Power saved:

1000 − 800

= 200 W

If operated for:

10 h

energy saved:

0.200 × 10

= 2 kWh

---

Energy Saving Over Time

Small improvements can become significant when repeated.

Suppose an efficient device saves:

0.5 kWh/day

Over one year:

0.5 × 365

= 182.5 kWh

If electricity costs:

$0.30/kWh

annual saving:

182.5 × 0.30

= $54.75

The longer a device operates, the more important efficiency can become.

---

Evaluating Whether an Upgrade Is Worthwhile

Suppose an efficient appliance costs:

$150 more

but saves:

$50 per year

Simple payback time:

payback time = additional cost / annual saving

payback time = 150/50

= 3 years

If the appliance lasts much longer than three years, the upgrade may provide financial savings after the payback period.

However, a complete evaluation might also consider maintenance, performance and changing electricity prices.

---

Energy Audits

An energy audit examines where energy is being consumed and identifies opportunities to reduce unnecessary consumption.

An audit might examine:

• lighting
• heating
• cooling
• appliances
• standby loads
• insulation
• operating schedules
• equipment efficiency

The largest energy consumers are often the best places to investigate first.

---

Example Household Energy Audit

Suppose daily consumption is:

air conditioning = 12 kWh

water heating = 5 kWh

lighting = 2 kWh

electronics = 3 kWh

other = 2 kWh

Total:

24 kWh/day

Air conditioning accounts for:

12/24 × 100%

= 50%

Improving cooling efficiency could therefore have a larger impact than focusing only on very small loads.

---

Reducing Peak Demand

Energy use can also be evaluated in terms of when electricity is required.

If many high-power devices operate simultaneously, the total power demand can become large.

For example:

air conditioner = 2.5 kW

oven = 3.0 kW

kettle = 2.0 kW

water heater = 3.5 kW

Total:

11.0 kW

Reducing simultaneous operation can reduce peak electrical demand even if total daily energy use remains similar.

---

Efficiency vs Conservation

Efficiency and conservation are related but different.

Efficiency

Obtaining more useful output from a given energy input.

Example:

replacing an inefficient lamp with an efficient LED.

Conservation

Reducing unnecessary energy use.

Example:

switching the lamp off when nobody needs it.

The most effective approach often combines both:

use efficient technology + avoid unnecessary use

---

Comparing Technologies Fairly

A fair comparison should ensure that devices provide approximately the same useful service.

For example, comparing two lamps only by wattage is incomplete.

Better questions include:

• Do they provide similar illumination?
• How much electrical power does each require?
• How long will each last?
• What is the total energy consumption?
• What is the operating cost?

Similarly, two air conditioners should be compared at similar cooling performance rather than simply comparing their electrical power.

---

Improving Efficiency

Efficiency can often be improved by reducing unwanted energy transfers.

Examples include:

Motors

Reduce friction and electrical resistance.

Buildings

Improve insulation.

Lighting

Use more efficient light sources.

Power transmission

Reduce current by using higher transmission voltage.

Electronics

Use efficient power supplies.

Heating systems

Reduce unwanted heat loss.

Cooling systems

Reduce heat entering the cooled space.

---

Common Mistakes

Mistake: Saying inefficient devices destroy energy.
Energy is conserved. It is transferred into less useful forms.

Mistake: Confusing efficiency with energy conservation.
Efficiency describes useful output compared with input. Conservation can also refer to reducing unnecessary use.

Mistake: Writing efficiency as more than 100%.
Ordinary energy-conversion efficiency cannot exceed 100%.

Mistake: Forgetting to multiply by 100% when expressing efficiency as a percentage.

Mistake: Using 80 instead of 0.80 in rearranged efficiency calculations.
Convert percentages to decimals when multiplying or dividing.

Mistake: Assuming lower power always means greater efficiency.
Useful output must also be considered.

Mistake: Assuming high efficiency automatically means low energy consumption.
Operating time and required output matter.

Mistake: Calling all thermal energy wasted.
Thermal energy is useful in heating devices.

Mistake: Ignoring standby consumption.
Small continuous loads can accumulate substantial energy use.

Mistake: Focusing only on small devices while ignoring major energy consumers.
Energy audits should prioritize large or long-running loads.

---

Key Terms

Efficiency — proportion of input energy or power transferred usefully.

Useful energy — energy transferred in the form required for the intended purpose.

Unwanted energy transfer — energy transferred in a way that does not contribute to the intended function.

Energy loss — common term for energy transferred into unwanted forms rather than destroyed.

Conservation of energy — principle that energy cannot be created or destroyed.

Energy consumption — amount of energy used or transferred over a period of time.

Kilowatt-hour (kWh) — unit of energy equal to 3.6 MJ.

Power — rate of energy transfer.

Standby power — electrical power consumed while a device is waiting or not performing its main function.

Energy-efficient technology — technology designed to provide a required useful output using less input energy.

Energy conservation — reduction of unnecessary energy consumption.

Sankey diagram — diagram representing energy transfers with arrow widths proportional to energy amounts.

Energy audit — systematic investigation of energy consumption and opportunities for improvement.

Payback time — time required for financial savings to recover an additional initial cost.

Life-cycle analysis — evaluation considering impacts across manufacture, operation and end of life.

Peak demand — maximum rate of electrical energy use during a particular period.

---

Key Takeaways

• Efficiency measures the proportion of input energy transferred usefully.
• efficiency = useful energy output / total energy input × 100%.
• Efficiency can also be calculated using power.
• Energy cannot be created or destroyed.
• Inefficient devices transfer more energy into unwanted forms.
• Thermal energy, sound and friction are common unwanted transfers.
• Whether an energy transfer is useful depends on the device's purpose.
• Sankey diagrams can represent useful and unwanted energy transfers.
• Electrical resistance can produce unwanted heating.
• Transmission losses are proportional to I²R.
• High-voltage transmission reduces current and therefore reduces heating losses.
• Energy consumption depends on both power and operating time.
• E = Pt.
• Household electrical energy is commonly measured in kWh.
• Low-power devices can consume significant energy when operated continuously.
• Efficient technologies should be compared based on similar useful outputs.
• LED lighting, efficient motors, insulation and efficient cooling systems can reduce energy consumption.
• Energy labels can help compare appliances.
• Efficiency and energy conservation are different but complementary approaches.
• Energy audits help identify where the greatest savings can be achieved.
• The most effective energy strategy is usually to combine efficient technology with reduced unnecessary use.

Check Your Understanding

1. Define efficiency.
2. Write the equation for efficiency using energy.
3. Write the equation for efficiency using power.
4. A device receives 500 J and produces 400 J of useful output. Calculate its efficiency.
5. Where does the remaining 100 J in Question 4 go?
6. A motor is 75% efficient and receives 2000 J. Calculate its useful energy output.
7. A machine must provide 1200 J of useful energy and is 80% efficient. Calculate the required input energy.
8. Explain why ordinary energy-conversion efficiency cannot exceed 100%.
9. Explain why the term "energy loss" does not mean that energy has been destroyed.
10. A wire carries 5 A and has a resistance of 2 Ω. Calculate the heating power.
11. If the current in Question 10 doubles, calculate the new heating power.
12. Explain why high-voltage transmission reduces energy losses.
13. A 2 kW appliance operates for 4 hours. Calculate its energy consumption in kWh.
14. A 50 W device operates continuously for 24 hours. Calculate its daily energy consumption in kWh.
15. Explain why a lower-power appliance is not necessarily more efficient.
16. Compare energy efficiency and energy conservation.
17. Suggest three ways a household could reduce energy used for heating or cooling.
18. A new appliance costs $200 more but saves $40 per year in electricity. Calculate its simple payback time.
19. Explain why an energy audit should usually focus first on high-power or long-running devices.
20. Evaluate the statement: "The best way to reduce electrical energy use is simply to buy lower-power appliances."

Electrical Power Systems

From Power Generation to Our Homes

An electrical power system is the large network used to generate, transmit, distribute, and control electrical energy.

A national or regional electricity system connects:

energy sources → generators → transformers → transmission lines → substations → distribution networks → consumers

Consumers include:

• homes
• schools
• hospitals
• offices
• factories
• transportation systems
• data centres

Unlike a simple classroom circuit, a national power grid can contain thousands of generators, substations, transmission lines, and millions of loads operating together.

---

Electrical Power Generation

Electrical energy must first be produced by a generator or another electrical energy source.

Many large power stations use generators that convert mechanical energy into electrical energy.

The mechanical energy can come from:

• steam turbines
• water turbines
• wind turbines
• gas turbines
• engines

The generator then converts the rotational mechanical energy into electrical energy using electromagnetic induction.

---

Electromagnetic Induction

A changing magnetic field can produce an emf in a conductor.

This principle is called:

electromagnetic induction

Generators use relative motion between:

• magnetic fields
• electrical conductors

to produce electrical energy.

In many generators, turbines rotate part of the generator, creating the changing magnetic conditions needed to generate electricity.

---

Energy Transformations in Power Stations

Power stations do not create energy.

They transform energy from one form into another.

For example:

Hydroelectric

gravitational potential → kinetic → mechanical → electrical

Wind

kinetic energy of wind → mechanical → electrical

Fossil fuel

chemical → thermal → mechanical → electrical

Nuclear

nuclear → thermal → mechanical → electrical

Solar photovoltaic

radiation → electrical

Energy is conserved throughout these transformations.

---

Thermal Power Stations

Many conventional power stations use thermal energy to produce steam.

A simplified sequence is:

energy source → thermal energy → steam → turbine → generator → electrical energy

The thermal energy may originate from:

• coal
• natural gas
• nuclear reactions
• biomass
• geothermal sources

The steam turns a turbine connected to a generator.

---

Hydroelectric Generation

Hydroelectric power stations use moving water.

Water stored at a height has gravitational potential energy.

As it moves downward:

gravitational potential energy → kinetic energy

The moving water turns turbines:

kinetic → mechanical energy

Generators then convert this into:

mechanical → electrical energy

---

Wind Generation

Wind turbines extract some of the kinetic energy of moving air.

The blades rotate, producing mechanical energy.

A generator converts this mechanical energy into electrical energy.

The transformation is approximately:

wind kinetic energy → rotational mechanical energy → electrical energy

Wind generation varies with wind conditions, so power systems must manage changes in output.

---

Solar Electricity

Solar photovoltaic cells operate differently from turbine-based generators.

They convert energy from solar radiation directly into electrical energy.

Solar output depends on factors including:

• sunlight intensity
• time of day
• weather
• season
• panel orientation
• shading

Large power systems can combine many different generation technologies.

---

Electrical Power

Electrical power is the rate at which electrical energy is transferred.

P = E/t

Electrical power can also be calculated using:

P = VI

where:

• P = power (W)
• V = voltage (V)
• I = current (A)

Large generators may produce power measured in:

• kilowatts (kW)
• megawatts (MW)
• gigawatts (GW)

Remember:

1 kW = 1000 W

1 MW = 1,000,000 W

1 GW = 1,000,000,000 W

---

Why Electricity Must Be Transmitted

Power stations are often located far from the places where electricity is needed.

For example:

• hydroelectric stations may be near large rivers
• wind farms may be in windy regions
• solar farms may require large open areas
• large thermal stations may be outside cities

Electrical energy therefore needs to be transported over large distances.

This is called electrical transmission.

---

The Transmission Network

The transmission network uses high-voltage power lines to transport electrical power over long distances.

Large transmission lines are often supported by towers or pylons.

The transmission network connects:

• generators
• substations
• major population centres
• industrial regions
• different parts of the grid

---

The Problem of Resistance

Transmission wires are good conductors, but they are not perfect conductors.

They have resistance.

When current flows through resistance, electrical energy is transferred into thermal energy.

The power transferred as heat is:

P_loss = I²R

where:

• P_loss = power lost as heating
• I = current
• R = resistance of transmission line

This heating represents energy that is not delivered to consumers.

---

Why Current Matters So Much

Notice that current is squared:

P_loss = I²R

Suppose a transmission line has:

R = 2 Ω

and carries:

I = 100 A

Then:

P_loss = 100² × 2

P_loss = 10,000 × 2

P_loss = 20,000 W

or:

20 kW

If the current doubles to 200 A:

P_loss = 200² × 2

P_loss = 80,000 W

or:

80 kW

Doubling current produces four times the heating loss.

---

Why High Voltage Is Used

The power being transmitted is approximately:

P = VI

Rearrange:

I = P/V

For a given transmitted power:

higher voltage → lower current

Lower current dramatically reduces:

I²R losses

Therefore, electrical power is transmitted over long distances using very high voltages.

This is one of the most important ideas in electrical power systems.

---

High-Voltage Example

Suppose:

P = 1,000,000 W

or:

1 MW

is being transmitted.

At 10,000 V

I = P/V

I = 1,000,000/10,000

I = 100 A

If the line resistance is:

R = 5 Ω

then:

P_loss = I²R

P_loss = 100² × 5

P_loss = 50,000 W

or:

50 kW

---

Transmitting the Same Power at Higher Voltage

Now transmit the same:

1 MW

at:

100,000 V

Current:

I = 1,000,000/100,000

I = 10 A

Heating loss:

P_loss = 10² × 5

P_loss = 500 W

Compare:

at 10 kV → 50,000 W lost

at 100 kV → 500 W lost

Increasing the voltage by a factor of 10 reduced the current by a factor of 10.

Because loss depends on I², heating loss decreased by a factor of:

100

---

High Voltage Improves Transmission Efficiency

Therefore:

high voltage → low current → lower I²R losses → greater transmission efficiency

This allows large amounts of electrical energy to be transported over hundreds or even thousands of kilometres.

However, extremely high voltages require:

• strong electrical insulation
• large clearances
• specialized equipment
• appropriate transmission towers
• careful safety systems

So transmission voltage is chosen by balancing efficiency, engineering requirements, safety, and cost.

---

Transformers

A transformer is a device that changes AC voltage.

Transformers are essential to electrical power systems.

They allow voltage to be:

• increased for transmission
• decreased for distribution and use

Transformers operate using electromagnetic induction.

---

Basic Transformer Structure

A simple transformer contains:

• primary coil
• secondary coil
• magnetic core

Alternating current in the primary coil produces a changing magnetic field.

The changing magnetic field passes through the core and induces an alternating emf in the secondary coil.

The coils are not normally connected directly by a conducting wire.

Energy is transferred through the changing magnetic field.

---

Why Transformers Require Changing Current

A transformer requires a changing magnetic field.

AC naturally produces a continuously changing magnetic field.

Steady DC does not continuously produce the changing magnetic flux required for normal transformer operation.

Therefore, conventional transformers are designed for AC.

---

Step-Up Transformers

A step-up transformer increases voltage.

For an ideal transformer:

V_secondary > V_primary

Step-up transformers are used near generating stations to increase voltage before long-distance transmission.

Higher voltage means lower current for the same power.

That reduces transmission losses.

---

Step-Down Transformers

A step-down transformer decreases voltage.

For an ideal transformer:

V_secondary < V_primary

Step-down transformers are used throughout the distribution network to reduce very high transmission voltages to levels suitable for local distribution and eventually consumers.

---

Transformer Turns Ratio

The voltage produced by a transformer depends on the number of turns in the coils.

For an ideal transformer:

V_s/V_p = N_s/N_p

where:

• V_s = secondary voltage
• V_p = primary voltage
• N_s = secondary turns
• N_p = primary turns

If the secondary has more turns:

N_s > N_p

then:

V_s > V_p

The transformer steps the voltage up.

---

Transformer Example

Suppose:

N_p = 500 turns

N_s = 5000 turns

V_p = 10,000 V

Then:

V_s/V_p = N_s/N_p

V_s/10,000 = 5000/500

V_s/10,000 = 10

Therefore:

V_s = 100,000 V

The transformer increases the voltage by a factor of 10.

---

Power in an Ideal Transformer

An ideal transformer does not create energy.

Therefore:

P_input = P_output

Since:

P = VI

we can write approximately:

V_pI_p = V_sI_s

This explains another important relationship.

If voltage increases:

current decreases

If voltage decreases:

current increases

for approximately the same transferred power.

---

Transformer Example with Current

Suppose an ideal transformer receives:

V_p = 10,000 V

I_p = 100 A

Input power:

P = VI

P = 10,000 × 100

P = 1,000,000 W

Suppose the output voltage is:

100,000 V

Then:

I_s = P/V_s

I_s = 1,000,000/100,000

I_s = 10 A

Voltage increased by a factor of 10 while current decreased by a factor of 10.

---

Real Transformers

Real transformers are not perfectly efficient.

Some energy is transferred into unwanted forms because of:

• resistance in the coils
• heating in the core
• magnetic effects
• vibration and sound

However, large power transformers can be highly efficient.

Energy conservation still applies:

input energy = useful output energy + unwanted energy transfers

---

From Generator to Consumer

A simplified electrical power system might operate like this:

Generator

↓

Step-up transformer

↓

High-voltage transmission lines

↓

Transmission substation

↓

Step-down transformer

↓

Distribution network

↓

Local transformer

↓

Homes and businesses

Voltage is changed several times as electricity moves through the system.

---

Transmission vs Distribution

These terms describe different parts of the grid.

Transmission

Moves large amounts of electrical power over long distances.

Typically uses very high voltages.

Distribution

Carries electrical power from substations to local consumers.

Uses lower voltages than major transmission networks.

The exact voltage levels depend on the electrical system.

---

Substations

A substation is a facility that helps control and distribute electrical power.

Substations may contain:

• transformers
• circuit breakers
• switches
• protection systems
• measurement equipment
• control systems

Substations connect different parts of the grid and allow operators to control power flow.

---

The National Power Grid

A power grid is an interconnected network of:

• generators
• transmission lines
• substations
• transformers
• distribution lines
• consumers

Rather than every city having a completely independent power supply, large interconnected networks allow electricity to be transferred between different areas.

---

The Grid as a Large Circuit

The national grid can be thought of as an enormous and complex electrical circuit.

The same fundamental principles still apply:

P = VI

V = IR

P_loss = I²R

Kirchhoff's laws and conservation principles also remain fundamental.

However, real power grids involve AC systems, multiple generators, changing loads, transformers, protection systems, and complex control.

---

Electricity Supply and Demand

Electrical generation must continuously respond to the amount of electrical power consumers require.

This demand changes throughout the day.

Demand may increase when:

• people wake up
• businesses begin operating
• air conditioning use increases
• cooking occurs
• industrial equipment operates

Demand may fall during periods of lower activity.

---

Peak Demand

Peak demand is the period when electricity consumption is highest.

During peak demand, the grid must provide enough power to meet the combined load.

If millions of devices are switched on simultaneously, the total power requirement can become extremely large.

Power systems therefore need enough:

• generation
• transmission capacity
• distribution capacity

to handle expected demand.

---

Power Balance

At any moment, the electrical system must maintain a balance between generation and consumption, with storage and other control systems increasingly helping manage that balance.

In simplified terms:

power generated ≈ power consumed + system losses

If supply and demand become seriously unbalanced, grid frequency and voltage can be affected.

---

Variable Renewable Energy

Wind and solar generation depend on environmental conditions.

Solar output changes with:

• daylight
• cloud cover
• season

Wind output changes with:

• wind speed
• weather systems

This means their electrical output can vary.

Power grids can manage this variability using combinations of:

• different generation sources
• transmission connections
• energy storage
• demand management
• forecasting
• flexible generation

---

Energy Storage

Energy storage can help balance electrical supply and demand.

Examples include:

• batteries
• pumped-storage hydroelectricity
• other mechanical or thermal storage systems

When electricity production exceeds immediate demand, some energy can be stored.

Later, the stored energy can help supply the grid when demand is higher.

---

Pumped-Storage Hydroelectricity

Pumped storage uses electricity to pump water to a higher reservoir when excess electrical energy is available.

Energy transformation during storage:

electrical → mechanical → gravitational potential

When electricity is needed:

gravitational potential → kinetic → mechanical → electrical

It effectively acts as a large-scale energy storage system.

---

Grid Interconnections

Power grids can be connected to neighboring regions.

Interconnections can allow electricity to flow between areas.

For example, one region may temporarily have:

• surplus generation

while another has:

• high demand

Electrical interconnections can improve flexibility and reliability.

---

Grid Reliability

A reliable electrical system should continue supplying electricity even when individual components fail.

Power networks can improve reliability through:

• multiple generators
• alternative transmission paths
• protection systems
• backup equipment
• automatic controls
• interconnected regions

This means electricity may sometimes reach a region through more than one possible transmission route.

---

Grid Protection

Electrical faults can produce extremely large currents.

Power systems therefore use protection equipment such as:

• circuit breakers
• protective relays
• monitoring systems
• grounding systems

When a serious fault occurs, protection systems can disconnect the affected section while allowing other parts of the grid to continue operating.

---

Transmission Line Resistance

Transmission losses can also be reduced by reducing resistance.

For a conductor:

R = ρL/A

where:

• ρ = resistivity
• L = length
• A = cross-sectional area

Resistance can be reduced by:

• using low-resistivity conductors
• increasing conductor cross-sectional area
• reducing unnecessary transmission distance where practical

However, thicker conductors require more material and cost more.

Engineering involves balancing performance and cost.

---

Why Not Use Infinite Voltage?

If higher voltage reduces transmission losses, it might seem that transmission voltage should simply be made as large as possible.

But higher voltages require:

• more insulation
• greater spacing
• larger towers
• specialized transformers
• more expensive equipment
• greater clearances

Very high electric fields can also create additional engineering problems.

Therefore, transmission systems use voltages that provide a practical balance between efficiency, safety, and cost.

---

Power Grid Efficiency

Suppose a generator produces:

1000 MW

and:

950 MW

reaches consumers.

Efficiency:

efficiency = useful output / input × 100%

efficiency = 950/1000 × 100%

efficiency = 95%

The remaining:

50 MW

has been transferred in other ways within the system, including electrical and transformer losses.

---

Household Circuits and the Grid

When you switch on an electrical appliance, it becomes one of many loads connected to the power system.

For example, a 2300 W kettle adds approximately:

2.3 kW

to electrical demand while operating.

One kettle is a tiny load compared with a national system.

Millions of appliances together create the total electrical demand that generators and the grid must supply.

---

From One Circuit to Millions

The principles studied in simple circuits scale into power systems.

Simple circuit

Battery → wires → resistor

Household circuit

Grid supply → distribution board → branch circuits → appliances

National grid

Generators → transformers → transmission → substations → distribution → millions of loads

The scale changes enormously, but electrical energy still obeys the same physical laws.

---

Evaluating Power Generation Methods

Different generation technologies have advantages and limitations.

Factors include:

• reliability
• cost
• environmental impact
• power output
• location
• fuel availability
• construction time
• operating lifetime
• ability to respond to changing demand

A complete power system usually involves a combination of technologies rather than a single type of generator.

---

Common Mistakes

Mistake: Saying power stations create energy.
They transform energy from other stores or sources into electrical energy.

Mistake: Saying transformers generate electricity.
Transformers change AC voltage; they do not provide the original energy source.

Mistake: Saying high voltage means more transmission loss.
For a fixed transmitted power, higher voltage allows lower current and therefore lower I²R losses.

Mistake: Forgetting that current is squared in P_loss = I²R.

Mistake: Assuming transmission wires have zero resistance.
Real conductors always have some resistance unless special conditions such as superconductivity apply.

Mistake: Saying a step-up transformer increases both voltage and current.
For approximately constant power, increasing voltage is accompanied by decreasing current.

Mistake: Assuming transformers work normally with steady DC.
Conventional transformers require changing magnetic flux and are therefore associated with AC.

Mistake: Confusing transmission with distribution.
Transmission generally moves large amounts of power over long distances; distribution delivers power locally.

Mistake: Thinking the national grid operates independently of household circuits.
Household loads contribute to the total demand on the grid.

---

Key Terms

Electrical power system — network used to generate, transmit, distribute, and control electrical energy.

Generator — device that converts mechanical energy into electrical energy through electromagnetic induction.

Electromagnetic induction — production of an emf due to changing magnetic flux.

Transmission — movement of large amounts of electrical power over long distances.

Distribution — delivery of electrical power from substations to local consumers.

Power grid — interconnected network of generators, transmission lines, substations, distribution systems, and consumers.

Transformer — device that changes AC voltage using electromagnetic induction.

Step-up transformer — transformer that increases voltage.

Step-down transformer — transformer that decreases voltage.

Substation — facility used to transform, switch, protect, measure, and control electrical power.

Transmission loss — energy transferred in unwanted ways during transmission, particularly resistive heating.

Peak demand — maximum electrical power demanded during a particular period.

Load — device or system consuming electrical power.

Grid interconnection — electrical connection allowing power exchange between regions.

Energy storage — system that stores energy for later use.

Pumped storage — storage method using gravitational potential energy of water.

---

Key Takeaways

• Electrical power systems connect generators to consumers.
• Many generators convert mechanical energy into electrical energy through electromagnetic induction.
• Power stations transform energy rather than create it.
• Electricity must often be transmitted long distances from generators to consumers.
• Transmission lines have resistance and therefore produce heating losses.
• Transmission heating losses are described by P_loss = I²R.
• Electrical power is P = VI.
• For the same transmitted power, increasing voltage decreases current.
• Lower current greatly reduces I²R transmission losses.
• This is why electrical power is transmitted at very high voltages.
• Transformers change AC voltage.
• Step-up transformers increase voltage for efficient transmission.
• Step-down transformers reduce voltage for distribution and use.
• Transformer operation depends on electromagnetic induction.
• An ideal transformer approximately conserves power: V_pI_p = V_sI_s.
• Transmission and distribution are different stages of the electrical system.
• Substations transform, control, switch, and protect electrical networks.
• National power grids connect many generators and millions of loads.
• Electricity supply must continually respond to changing demand.
• Renewable generation, storage, interconnections, and control systems can work together to maintain a reliable grid.
• The circuit principles studied in small circuits remain fundamental to large electrical power systems.

Check Your Understanding

1. What is an electrical power system?
2. Describe the main energy transformation in an electrical generator.
3. What physical principle allows generators to produce an emf?
4. Describe the energy transformations in a hydroelectric power station.
5. Explain the difference between electrical transmission and distribution.
6. Why do transmission wires cause energy losses?
7. Write the equation for heating power loss in a transmission line.
8. A transmission line carries 200 A and has a resistance of 3 Ω. Calculate the power lost as heating.
9. If the current in Question 8 is reduced to 100 A, calculate the new power loss.
10. Explain why reducing current has such a large effect on transmission losses.
11. A transmission system transfers 10 MW at 10 kV. Calculate the current using P = VI.
12. Calculate the current if the same 10 MW is transmitted at 100 kV.
13. Explain why high-voltage transmission is more efficient.
14. What is the purpose of a step-up transformer?
15. What is the purpose of a step-down transformer?
16. Explain qualitatively how a transformer transfers electrical energy between its primary and secondary coils.
17. Why are conventional transformers associated with AC rather than steady DC?
18. Describe the journey of electrical energy from a generator to a household appliance.
19. Explain how switching on millions of household appliances affects demand on the national power grid.
20. Explain how generators, transformers, transmission lines, substations, distribution networks, storage systems, and consumers work together as one electrical power system.