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)

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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.

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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.

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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)

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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.

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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

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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.

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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

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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.

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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.

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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.

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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

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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.

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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.

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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%

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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%

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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.

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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.

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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

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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

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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.

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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

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.