Power

What you'll learn

What power means in physics: energy transferred each second.
How to calculate the power of a circuit device using $P = V I$ .
How to use resistance in power calculations with $P = I^2R$ .
How to link power to the total energy transferred over time.

Power: the big idea

In everyday language, “powerful” often means “strong”. In physics, it has a very precise meaning.

Definition

Power

Power is the rate at which energy is transferred. In other words, it tells you how much energy is transferred each second. Power is measured in watts (W), where 1 watt means 1 joule per second.

A 100 W device transfers energy twice as quickly as a 50 W device. That does not automatically mean it is more efficient — it just means the energy transfer happens faster.

For any device:

\frac{E}{t}

where:

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

Rearranged:

E = P t

Key Idea

Power means energy per second

A higher power means a faster rate of energy transfer, not necessarily more total energy overall. Total energy also depends on how long the device is used for.

Power in circuit devices

A circuit device is any component that transfers electrical energy to another store or pathway. Examples include:

a lamp, which transfers electrical energy to light and thermal energy
a heater, which transfers electrical energy mainly to thermal energy
a motor, which transfers electrical energy to kinetic energy, with some wasted as thermal energy and sound

To understand power in circuits, you need two key quantities.

Current

Current is the rate of flow of electric charge. Electric charge is measured in coulombs (C), and current is measured in amperes (A). You can say “amps” for amperes.

A current flows through a component.

Potential difference

Potential difference, often shortened to p.d., is the energy transferred by each coulomb of charge passing through a component. It is measured in volts (V).

A potential difference is measured across a component.

Circuit lamp showing current through the lamp, potential difference across it, and power transferred as light and thermal energy

Common Mistake

Through vs across

Current goes through a component. Potential difference is measured across a component. This wording is very common in GCSE questions.

The equation $P = V I$

The power transferred by a circuit device depends on:

the potential difference across it
the current through it

The equation is:

P = V I

This means:

difference×current\text{power} = \text{potential difference} \times \text{current}

where:

$P$ is power in watts (W)
$V$ is potential difference in volts (V)
$I$ is current in amperes (A)

Why this equation makes sense

Potential difference tells you the energy transferred per coulomb of charge. Current tells you how many coulombs pass each second.

So:

JC×Cs=Js=W\frac{\text{J}}{\text{C}} \times \frac{\text{C}}{\text{s}} = \frac{\text{J}}{\text{s}} = \text{W}

That is why multiplying potential difference by current gives power.

Example

Calculating power from potential difference and current

A lamp has a potential difference of 12 V across it and a current of 0.50 A through it. Calculate its power.

Choose $P = V I$ because the question gives potential difference and current.
Substitute the values into the equation:
$12\ \text{V} \times 0.50\ \text{A}$
Calculate the power:
$6.0\ \text{W}$
Interpret the answer: the lamp transfers 6.0 J of energy every second.

Using resistance: the equation $P = I^2R$

Resistance is a measure of how difficult it is for current to flow through a component. Resistance is measured in ohms (Ω).

You already know that:

V = I R

If we substitute $V = I R$ into $P = V I$ :

P=VIP=(IR)IP=I2R\begin{aligned} P &= VI \\ P &= (IR)I \\ P &= I^2R \end{aligned}

So the second power equation is:

P = I^2R

This means:

power=(current)2×resistance\text{power} = (\text{current})^2 \times \text{resistance}

Key Idea

Current has a squared effect

For a fixed resistance, doubling the current makes the power four times bigger, because the current is squared in $P = I^2R$ .

Example

Calculating power from current and resistance

An electric heater has a resistance of 18 Ω. The current through it is 4.0 A. Calculate the power transferred.

Choose $P = I^2R$ because the question gives current and resistance.
Square the current first:
$A2I^2 = (4.0\ \text{A})^2 = 16\ \text{A}^2$
Multiply by the resistance:
$16\ \text{A}^2 \times 18\ \Omega$
Calculate the power:
$288\ \text{W}$

Common Mistake

Forgetting to square the current

In $P = I^2R$ , square the current before multiplying by the resistance. For example, if the current is 4.0 A, use 16, not 4.0.

Choosing the right power equation

You will usually choose the equation based on the quantities in the question.

Use $P = V I$ when you know:

power, potential difference, and current
or you need to find one of those three quantities

Use $P = I^2R$ when you know:

power, current, and resistance
or you need to find one of those three quantities

Tip

Equation choice

If the question gives voltage and current, use $P = V I$ . If it gives current and resistance, use $P = I^2R$ .

Rearranging $P = V I$

From:

P = V I

you can rearrange to find current:

\frac{P}{V}

or potential difference:

\frac{P}{I}

Example

Finding current from power and potential difference

A small motor transfers energy at a power of 24 W when connected to a 6.0 V supply. Calculate the current through the motor.

Choose $P = V I$ because the question gives power and potential difference.
Rearrange to make current the subject:
$\frac{P}{V}$
Substitute the values:
$\frac{24\ \text{W}}{6.0\ \text{V}}$
Calculate the current:
$4.0\ \text{A}$

Linking circuit power to energy over time

Once you have calculated the power of a device, you can calculate the total energy transferred if you know how long it operates for.

Use:

E = P t

For a circuit device where $P = V I$ , you can also think of it as:

E = V I t

But at GCSE, it is usually clearest to calculate the power first, then multiply by time.

Common Mistake

Use seconds for time

Power is measured in watts, and 1 W means 1 J/s. So when using $E = P t$ , time must be in seconds, not minutes or hours.

Example

Calculating energy transferred over time

A 9.0 V motor has a current of 0.80 A through it. It runs for 3.0 minutes. Calculate the energy transferred.

First calculate the power using $P = V I$ :
$9.0\ \text{V} \times 0.80\ \text{A} = 7.2\ \text{W}$
Convert the time into seconds:

3.0 minutes = 180 s
Use $E = P t$ :
$7.2\ \text{W} \times 180\ \text{s}$
Calculate the energy transferred:
$1296\ \text{J}$

So the motor transfers about 1300 J of energy.

Quick unit summary

Power, $P$ , is measured in watts (W).
Potential difference, $V$ , is measured in volts (V).
Current, $I$ , is measured in amperes (A).
Resistance, $R$ , is measured in ohms (Ω).
Energy, $E$ , is measured in joules (J).
Time, $t$ , is measured in seconds (s).

Exam technique

In the exam

Identify what the question gives you: potential difference, current, resistance, power, energy, or time.
Choose the equation that uses those quantities: $P = V I$ , $P = I^2R$ , or $E = P t$ if energy over time is involved.
Substitute values with SI units, especially converting time into seconds before calculating energy.

Self review

Check yourself

What does it mean if one device has a higher power than another?
When should you use $P = V I$ rather than $P = I^2R$ ?
Why must time be in seconds when using $E = P t$ ?

Power

What you'll learn

What power means in physics: energy transferred each second.
How to calculate the power of a circuit device using $P = V I$ .
How to use resistance in power calculations with $P = I^2R$ .
How to link power to the total energy transferred over time.

Power: the big idea

In everyday language, “powerful” often means “strong”. In physics, it has a very precise meaning.

Definition

Power

A 100 W device transfers energy twice as quickly as a 50 W device. That does not automatically mean it is more efficient — it just means the energy transfer happens faster.

For any device:

\frac{E}{t}

where:

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

Rearranged:

E = P t

Key Idea

Power means energy per second

A higher power means a faster rate of energy transfer, not necessarily more total energy overall. Total energy also depends on how long the device is used for.

Power in circuit devices

A circuit device is any component that transfers electrical energy to another store or pathway. Examples include:

a lamp, which transfers electrical energy to light and thermal energy
a heater, which transfers electrical energy mainly to thermal energy
a motor, which transfers electrical energy to kinetic energy, with some wasted as thermal energy and sound

To understand power in circuits, you need two key quantities.

Current

Current is the rate of flow of electric charge. Electric charge is measured in coulombs (C), and current is measured in amperes (A). You can say “amps” for amperes.

A current flows through a component.

Potential difference

Potential difference, often shortened to p.d., is the energy transferred by each coulomb of charge passing through a component. It is measured in volts (V).

A potential difference is measured across a component.

Circuit lamp showing current through the lamp, potential difference across it, and power transferred as light and thermal energy

Common Mistake

Through vs across

Current goes through a component. Potential difference is measured across a component. This wording is very common in GCSE questions.

The equation $P = V I$

The power transferred by a circuit device depends on:

the potential difference across it
the current through it

The equation is:

P = V I

This means:

difference×current\text{power} = \text{potential difference} \times \text{current}

where:

$P$ is power in watts (W)
$V$ is potential difference in volts (V)
$I$ is current in amperes (A)

Why this equation makes sense

Potential difference tells you the energy transferred per coulomb of charge. Current tells you how many coulombs pass each second.

So:

JC×Cs=Js=W\frac{\text{J}}{\text{C}} \times \frac{\text{C}}{\text{s}} = \frac{\text{J}}{\text{s}} = \text{W}

That is why multiplying potential difference by current gives power.

Example

Calculating power from potential difference and current

A lamp has a potential difference of 12 V across it and a current of 0.50 A through it. Calculate its power.

Choose $P = V I$ because the question gives potential difference and current.
Substitute the values into the equation:
$12\ \text{V} \times 0.50\ \text{A}$
Calculate the power:
$6.0\ \text{W}$
Interpret the answer: the lamp transfers 6.0 J of energy every second.

Using resistance: the equation $P = I^2R$

Resistance is a measure of how difficult it is for current to flow through a component. Resistance is measured in ohms (Ω).

You already know that:

V = I R

If we substitute $V = I R$ into $P = V I$ :

P=VIP=(IR)IP=I2R\begin{aligned} P &= VI \\ P &= (IR)I \\ P &= I^2R \end{aligned}

So the second power equation is:

P = I^2R

This means:

power=(current)2×resistance\text{power} = (\text{current})^2 \times \text{resistance}

Key Idea

Current has a squared effect

For a fixed resistance, doubling the current makes the power four times bigger, because the current is squared in $P = I^2R$ .

Example

Calculating power from current and resistance

An electric heater has a resistance of 18 Ω. The current through it is 4.0 A. Calculate the power transferred.

Choose $P = I^2R$ because the question gives current and resistance.
Square the current first:
$A2I^2 = (4.0\ \text{A})^2 = 16\ \text{A}^2$
Multiply by the resistance:
$16\ \text{A}^2 \times 18\ \Omega$
Calculate the power:
$288\ \text{W}$

Common Mistake

Forgetting to square the current

In $P = I^2R$ , square the current before multiplying by the resistance. For example, if the current is 4.0 A, use 16, not 4.0.

Choosing the right power equation

You will usually choose the equation based on the quantities in the question.

Use $P = V I$ when you know:

power, potential difference, and current
or you need to find one of those three quantities

Use $P = I^2R$ when you know:

power, current, and resistance
or you need to find one of those three quantities

Tip

Equation choice

If the question gives voltage and current, use $P = V I$ . If it gives current and resistance, use $P = I^2R$ .

Rearranging $P = V I$

From:

P = V I

you can rearrange to find current:

\frac{P}{V}

or potential difference:

\frac{P}{I}

Example

Finding current from power and potential difference

A small motor transfers energy at a power of 24 W when connected to a 6.0 V supply. Calculate the current through the motor.

Choose $P = V I$ because the question gives power and potential difference.
Rearrange to make current the subject:
$\frac{P}{V}$
Substitute the values:
$\frac{24\ \text{W}}{6.0\ \text{V}}$
Calculate the current:
$4.0\ \text{A}$

Linking circuit power to energy over time

Once you have calculated the power of a device, you can calculate the total energy transferred if you know how long it operates for.

Use:

E = P t

For a circuit device where $P = V I$ , you can also think of it as:

E = V I t

But at GCSE, it is usually clearest to calculate the power first, then multiply by time.

Common Mistake

Use seconds for time

Power is measured in watts, and 1 W means 1 J/s. So when using $E = P t$ , time must be in seconds, not minutes or hours.

Example

Calculating energy transferred over time

A 9.0 V motor has a current of 0.80 A through it. It runs for 3.0 minutes. Calculate the energy transferred.

First calculate the power using $P = V I$ :
$9.0\ \text{V} \times 0.80\ \text{A} = 7.2\ \text{W}$
Convert the time into seconds:

3.0 minutes = 180 s
Use $E = P t$ :
$7.2\ \text{W} \times 180\ \text{s}$
Calculate the energy transferred:
$1296\ \text{J}$

So the motor transfers about 1300 J of energy.

Quick unit summary

Power, $P$ , is measured in watts (W).
Potential difference, $V$ , is measured in volts (V).
Current, $I$ , is measured in amperes (A).
Resistance, $R$ , is measured in ohms (Ω).
Energy, $E$ , is measured in joules (J).
Time, $t$ , is measured in seconds (s).

Exam technique

In the exam

Identify what the question gives you: potential difference, current, resistance, power, energy, or time.
Choose the equation that uses those quantities: $P = V I$ , $P = I^2R$ , or $E = P t$ if energy over time is involved.
Substitute values with SI units, especially converting time into seconds before calculating energy.

Self review

Check yourself

What does it mean if one device has a higher power than another?
When should you use $P = V I$ rather than $P = I^2R$ ?
Why must time be in seconds when using $E = P t$ ?

Power

What you'll learn

Power: the big idea

Power in circuit devices

Current

Potential difference

The equation $P = V I$

Why this equation makes sense

Using resistance: the equation $P = I^2R$

Choosing the right power equation

Rearranging $P = V I$

Linking circuit power to energy over time

Quick unit summary

You've reached the end

Power

What you'll learn

Power: the big idea

Power in circuit devices

Current

Potential difference

The equation $P = V I$

Why this equation makes sense

Using resistance: the equation $P = I^2R$

Choosing the right power equation

Rearranging $P = V I$

Linking circuit power to energy over time

Quick unit summary

You've reached the end

Power

What you'll learn

Power: the big idea

Power in circuit devices

Current

Potential difference

The equation P=VIP = VIP=VI

Why this equation makes sense

Using resistance: the equation P=I2RP = I^2RP=I2R

Choosing the right power equation

Rearranging P=VIP = VIP=VI

Linking circuit power to energy over time

Quick unit summary

You've reached the end

Power Revision Guide

Power

What you'll learn

Power: the big idea

Power in circuit devices

Current

Potential difference

The equation P=VIP = VIP=VI

Why this equation makes sense

Using resistance: the equation P=I2RP = I^2RP=I2R

Choosing the right power equation

Rearranging P=VIP = VIP=VI

Linking circuit power to energy over time

Quick unit summary

You've reached the end

Power Revision Guide

The equation $P = V I$

Using resistance: the equation $P = I^2R$

Rearranging $P = V I$

The equation $P = V I$

Using resistance: the equation $P = I^2R$

Rearranging $P = V I$