3. Electrical Power

Electrical Power

Electrical power is the rate at which electrical energy is transferred by a device or circuit.

Every electrical device transfers energy. For example:

• a lamp transfers electrical energy into light and thermal energy
• a heater transfers electrical energy into thermal energy
• a motor transfers electrical energy into mechanical energy
• a speaker transfers electrical energy into sound
• a charger transfers electrical energy into energy stored in a battery

The power rating tells us how quickly this energy is transferred.

Electrical Power

Power is the rate of energy transfer:

P = E/t

where:

• P = power in watts (W)
• E = energy transferred in joules (J)
• t = time in seconds (s)

For electrical circuits, power can also be calculated using:

P = IV

where:

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

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

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The Watt

Electrical power is measured in watts (W).

1 W = 1 J/s

Therefore, a 60 W device transfers:

60 J of energy every second

A 2000 W heater transfers:

2000 J every second

A higher power rating means energy is transferred at a greater rate.

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Current, Voltage, and Power

The equation:

P = IV

shows that electrical power depends on both:

• current
• voltage

If voltage remains constant:

greater current → greater power

If current remains constant:

greater voltage → greater power

For example:

Current = 2 A
Voltage = 12 V

P = IV

P = 2 × 12

P = 24 W

The device transfers electrical energy at a rate of 24 J/s.

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Worked Example: Simple Circuit

A lamp operates at:

V = 12 V

and draws:

I = 3 A

Calculate its power.

P = IV

P = 3 × 12

P = 36 W

The lamp transfers 36 J of energy each second.

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Worked Example: Electric Motor

A motor operates at:

24 V

and draws:

5 A

Calculate the electrical power supplied to the motor.

P = IV

P = 5 × 24

P = 120 W

The motor receives electrical energy at a rate of:

120 J/s

Not all of this necessarily becomes useful mechanical power because the motor is not perfectly efficient.

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Rearranging P = IV

Starting with:

P = IV

we can rearrange the equation.

To calculate current:

I = P/V

To calculate voltage:

V = P/I

So we have:

P = IV

I = P/V

V = P/I

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Worked Example: Finding Current

An electrical heater has a power rating of:

1200 W

and operates at:

240 V

Calculate the current.

I = P/V

I = 1200/240

I = 5 A

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Worked Example: Finding Voltage

A device operates at:

60 W

and draws:

2.5 A

Calculate the voltage.

V = P/I

V = 60/2.5

V = 24 V

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Why P = IV?

Recall that voltage represents energy transferred per unit charge:

V = E/Q

Current represents charge flowing per unit time:

I = Q/t

Power is:

P = E/t

Since:

E = VQ

then:

P = VQ/t

But:

Q/t = I

Therefore:

P = IV

This connects electrical power directly to the movement of charge through a potential difference.

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Power Ratings

Most electrical devices have a power rating.

The rating tells us the rate at which the device transfers energy when operating under its rated conditions.

For example:

These are illustrative values; actual devices vary considerably.

What Does a 2000 W Rating Mean?

Suppose a kettle is rated:

2000 W

This means that while operating at its rated power, it transfers energy at:

2000 J/s

In 1 second:

2000 J

In 10 seconds:

20,000 J

In 60 seconds:

120,000 J

Therefore, power tells us how quickly a device transfers energy.

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Electrical Energy Consumption

Because:

P = E/t

we can rearrange:

E = Pt

This allows us to calculate the energy transferred by an electrical device.

where:

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

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Worked Example: Electric Heater

A 1500 W heater operates for 5 minutes.

First convert time:

5 min = 300 s

Then:

E = Pt

E = 1500 × 300

E = 450,000 J

or:

E = 450 kJ

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Worked Example: Lamp

A 20 W lamp operates for 3 hours.

Convert time:

3 h = 10,800 s

Then:

E = Pt

E = 20 × 10,800

E = 216,000 J

or:

E = 216 kJ

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Energy Depends on Power and Time

A device with a high power rating transfers energy quickly.

However, total energy consumption depends on both power and operating time.

Consider two devices.

Device A

Power = 2000 W
Time = 60 s

E = 2000 × 60

E = 120,000 J

Device B

Power = 100 W
Time = 3600 s

E = 100 × 3600

E = 360,000 J

Even though Device B has much lower power, it transfers more total energy because it operates for much longer.

Therefore:

high power does not automatically mean greater total energy consumption

Operating time matters.

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Kilowatts

Household electrical devices are often rated in watts or kilowatts.

1 kW = 1000 W

Examples:

500 W = 0.5 kW

1500 W = 1.5 kW

2000 W = 2 kW

3500 W = 3.5 kW

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Kilowatt-Hours

Electricity use in homes is commonly measured in kilowatt-hours (kWh) rather than joules.

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

1 kWh is the energy transferred by a 1 kW device operating for 1 hour.

Therefore:

energy (kWh) = power (kW) × time

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Understanding 1 kWh

Suppose a 1 kW heater operates for 1 hour.

Energy:

E = Pt

E = 1 kW × 1 h

E = 1 kWh

The same energy could be transferred by:

• a 2 kW device for 0.5 h
• a 0.5 kW device for 2 h
• a 0.25 kW device for 4 h

Each transfers:

1 kWh

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Converting kWh to Joules

We know:

1 kW = 1000 W

and:

1 h = 3600 s

Therefore:

1 kWh = 1000 × 3600 J

1 kWh = 3,600,000 J

or:

1 kWh = 3.6 MJ

This is a useful conversion.

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Worked Example: Kettle in kWh

A 2 kW kettle operates for 6 minutes.

Convert time to hours:

6 min = 0.1 h

Then:

E = Pt

E = 2 × 0.1

E = 0.2 kWh

In joules:

0.2 × 3.6 MJ = 0.72 MJ

or:

720,000 J

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Worked Example: Air Conditioner

An air conditioner operates at an average electrical power of 1.5 kW for 8 hours.

Calculate its energy consumption.

E = Pt

E = 1.5 × 8

E = 12 kWh

The air conditioner uses 12 kWh of electrical energy over that period.

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Electrical Energy Cost

If electricity costs a certain amount per kWh:

cost = energy used × price per kWh

For example, suppose a device uses:

5 kWh

and electricity costs:

$0.30 per kWh

Then:

cost = 5 × 0.30

cost = $1.50

This is why both power rating and operating time affect electricity bills.

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Comparing Electrical Devices

Suppose two heaters operate for the same time.

Heater A:

1000 W

Heater B:

2000 W

Heater B transfers energy twice as quickly.

If both operate for 10 minutes:

Heater A:

E = 1000 × 600

E = 600,000 J

Heater B:

E = 2000 × 600

E = 1,200,000 J

The 2000 W heater transfers twice as much energy during the same period.

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Higher Power Can Mean Shorter Operating Time

However, a higher-power appliance may complete a task more quickly.

Suppose two ideal heaters must transfer:

600,000 J

Heater A:

P = 1000 W

t = E/P

t = 600,000/1000

t = 600 s

Heater B:

P = 2000 W

t = 600,000/2000

t = 300 s

The more powerful heater completes the energy transfer in half the time.

This demonstrates why power and total energy consumption should not be confused.

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Electrical Power in Heating Devices

Devices designed to produce heat often have relatively high power ratings.

Examples include:

• kettles
• ovens
• heaters
• toasters
• hair dryers
• irons

They need to transfer large amounts of thermal energy in relatively short periods.

Electrical Power in Motors

Electric motors transfer:

electrical energy → mechanical energy

Examples include motors in:

• fans
• elevators
• electric vehicles
• washing machines
• pumps
• power tools

A motor's electrical input power can be calculated using:

Pinput = IV

Its useful mechanical output power may be calculated using:

Poutput = W/t

or:

Poutput = Fv

The output is normally less than the input because real motors are not perfectly efficient.

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Worked Example: Electric Motor

A motor operates at:

120 V

and draws:

10 A

Electrical input power:

P = IV

P = 10 × 120

P = 1200 W

Suppose its useful mechanical output power is:

960 W

Efficiency:

efficiency = useful output power / input power × 100

efficiency = 960/1200 × 100

efficiency = 80%

The remaining power is transferred mainly into thermal energy and sound.

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Power in Simple Circuits

Suppose a resistor has:

V = 6 V

across it and:

I = 0.5 A

through it.

Power:

P = IV

P = 0.5 × 6

P = 3 W

The resistor transfers electrical energy at a rate of:

3 J/s

Much of this energy becomes thermal energy.

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Electrical Power and Resistance

Using Ohm's law:

V = IR

we can combine this with:

P = IV

Substituting V = IR:

P = I × IR

Therefore:

P = I²R

Alternatively:

I = V/R

Substitute into P = IV:

P = V × V/R

Therefore:

P = V²/R

So three useful electrical power equations are:

P = IV

P = I²R

P = V²/R

For this topic, P = IV is the central equation, but the other forms can be useful when resistance is known.

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Worked Example: Power and Resistance

A 10 Ω resistor carries a current of:

2 A

Use:

P = I²R

P = 2² × 10

P = 40 W

The resistor transfers electrical energy at a rate of 40 J/s.

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Worked Example: Voltage and Resistance

A 12 Ω resistor is connected across:

24 V

Use:

P = V²/R

P = 24²/12

P = 576/12

P = 48 W

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Power and Current in Household Devices

At a fixed supply voltage:

I = P/V

This means higher-power appliances generally draw larger currents.

For example, compare two devices operating at 230 V.

230 W Device

I = 230/230

I = 1 A

2300 W Device

I = 2300/230

I = 10 A

The higher-power device requires a much greater current.

This is one reason electrical wiring and protective devices must be appropriate for the current a circuit carries.

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Power Ratings and Safe Operation

Electrical devices are designed to operate under particular electrical conditions.

A rating label may include:

• voltage
• current
• power
• frequency
• energy consumption information

For example, a label might indicate:

230 V

1500 W

This tells us that when operating as designed at the rated voltage, the appliance uses electrical power at approximately 1500 W.

Why Device Ratings Matter

Power ratings help users and engineers determine:

• how quickly a device transfers energy
• how much electrical energy it may consume
• how much current it may draw
• appropriate electrical connections
• likely operating costs
• energy-efficiency considerations

A power rating therefore provides important information about both performance and energy use.

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Power and Efficiency

Electrical devices rarely convert all input energy into the desired output.

For example, an electric motor might receive:

1000 W electrical power

but provide:

850 W mechanical power

The remaining:

150 W

may be transferred into:

• thermal energy
• sound
• vibration

Efficiency:

efficiency = 850/1000 × 100

efficiency = 85%

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Energy Flow Example

Consider a lamp receiving:

10 W electrical power

Suppose:

8 W → light

and:

2 W → thermal energy

Then:

10 W input = 8 W useful + 2 W other transfers

Energy is conserved.

Over 10 seconds:

Input energy:

E = Pt

E = 10 × 10

E = 100 J

Useful energy:

8 × 10 = 80 J

Thermal energy:

2 × 10 = 20 J

Therefore:

100 J = 80 J + 20 J

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Choosing the Correct Equation

Use:

P = IV

when you know current and voltage.

Use:

P = E/t

when you know energy and time.

Use:

E = Pt

when you know power and operating time.

Use:

E(kWh) = P(kW) × t

when calculating household electricity consumption.

Use:

P = I²R

when current and resistance are known.

Use:

P = V²/R

when voltage and resistance are known.

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Multi-Step Example

A heater operates at:

230 V

and draws:

8 A

It operates for:

15 minutes

Calculate Power

P = IV

P = 8 × 230

P = 1840 W

Convert Time

15 min = 900 s

Calculate Energy

E = Pt

E = 1840 × 900

E = 1,656,000 J

or:

E = 1.656 MJ

Alternatively:

P = 1.84 kW

t = 0.25 h

Therefore:

E = 1.84 × 0.25

E = 0.46 kWh

Both calculations describe the same energy transfer.

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Common Mistakes

Confusing Power and Energy

Power is measured in:

watts

Energy is measured in:

joules or kilowatt-hours.

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Thinking kWh Is a Unit of Power

It is not.

kW = power

kWh = energy

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Forgetting Time Conversion

For joule calculations:

1 min = 60 s

1 h = 3600 s

For kWh calculations, time should normally be in hours.

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Forgetting to Convert Watts to Kilowatts

For kWh:

1000 W = 1 kW

Therefore:

2500 W = 2.5 kW

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Mixing Units

Do not calculate:

2000 W × 3 h

and call the answer joules.

Use compatible units:

W × s → J

or:

kW × h → kWh

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Assuming High Power Always Means High Energy Consumption

A high-power device operating briefly may use less energy than a low-power device operating for many hours.

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Confusing Current and Voltage

Current measures the rate of charge flow.

Voltage measures energy transferred per unit charge.

Power depends on both:

P = IV

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Ignoring Efficiency

Electrical input power is not always equal to useful output power.

Real devices transfer some energy into other forms.

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Check Your Understanding

1. Define electrical power.
2. State the SI unit of electrical power.
3. What does a power of 1 W mean?
4. State the equation relating power, current, and voltage.
5. A device operates at 12 V and draws 4 A. Calculate its power.
6. A motor operates at 24 V and draws 8 A. Calculate its electrical input power.
7. A 1500 W heater operates at 250 V. Calculate the current.
8. A 60 W device draws 2 A. Calculate its operating voltage.
9. Explain what a 2000 W power rating means.
10. A 500 W device operates for 20 s. Calculate the energy transferred.
11. A 2 kW heater operates for 5 minutes. Calculate the energy transferred in joules.
12. Calculate the answer to Question 11 in kWh.
13. What is the difference between kW and kWh?
14. Convert 1 kWh into joules.
15. A 1.5 kW air conditioner operates for 6 h. Calculate its energy consumption in kWh.
16. A 100 W device operates for 10 h. How much energy does it consume in kWh?
17. Explain why a lower-power device can sometimes consume more energy than a higher-power device.
18. A 10 Ω resistor carries 3 A. Calculate its power.
19. A 20 Ω resistor has 40 V across it. Calculate its power.
20. A motor receives 2000 W of electrical power and produces 1600 W of useful mechanical power. Calculate its efficiency.
21. How much power is transferred into other forms in Question 20?
22. A heater operates at 240 V and 10 A for 30 minutes. Calculate its power.
23. Calculate the energy consumed by the heater in Question 22 in kWh.
24. If electricity costs $0.30 per kWh, calculate the operating cost for Question 23.
25. Explain why power ratings are useful when comparing electrical devices.

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Key Terms

Electrical power — Rate at which electrical energy is transferred.

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

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

Kilowatt (kW) — Unit of power equal to 1000 W.

Energy — Quantity that can be stored and transferred.

Joule (J) — SI unit of energy.

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

Current (I) — Rate of flow of electric charge, measured in amperes.

Potential difference (V) — Energy transferred per unit charge, measured in volts.

Resistance (R) — Opposition to current in a circuit, measured in ohms.

Electrical energy — Energy transferred through electrical processes.

Input power — Rate at which energy enters a device.

Useful output power — Rate at which energy is transferred into the intended output.

Efficiency — Fraction of input power or energy transferred usefully.

Power consumption — Rate at which a device receives or transfers electrical energy.

Energy consumption — Total electrical energy transferred during a period of operation.

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Key Takeaways

• Electrical power is the rate of electrical energy transfer.
• Electrical power is measured in watts.
• 1 W = 1 J/s.
• The main electrical power equation is P = IV.
• Power increases if current increases while voltage remains constant.
• Power increases if voltage increases while current remains constant.
• The equation can be rearranged to I = P/V and V = P/I.
• A device's power rating tells us how quickly it transfers energy under its rated conditions.
• Energy consumption depends on both power and operating time.
• Energy can be calculated using E = Pt.
• For household electricity calculations, E(kWh) = P(kW) × t.
• kW is a unit of power, while kWh is a unit of energy.
• 1 kWh = 3.6 MJ.
• High-power appliances transfer energy rapidly, but they do not necessarily consume more total energy if they operate for shorter periods.
• Combining P = IV with Ohm's law gives P = I²R and P = V²/R.
• Higher-power devices generally draw greater current when operated at the same voltage.
• Electrical input power can be compared with useful output power to determine efficiency.
• Real electrical devices transfer some energy into unwanted forms, commonly thermal energy.
• Power ratings are useful for comparing device performance, estimating energy consumption, and understanding electrical requirements.

The central relationship is:

P = IV

and for energy consumption:

E = Pt

So remember:

power tells us how fast energy is transferred

while:

energy tells us how much has been transferred in total.