Electrical power

What you'll learn

What electrical power means: the energy transferred each second by a circuit device.
How electric current (flow of charge) and potential difference (energy transferred per unit charge) affect power.
How to use $\frac{E}{t}$ , $\times V$ , $I^2 \times R$ , and $\times V \times t$ .
How to choose the right equation and keep units under control.

The idea: energy is transferred in circuits

A circuit device, such as a lamp, motor, heater or resistor, transfers energy. For example:

a lamp transfers energy electrically to light and thermal stores
a motor transfers energy electrically to kinetic and thermal stores
a heater transfers energy electrically to thermal stores

The symbol for energy transferred is $E$ . It is measured in joules, J.

To understand electrical power, you need three earlier circuit ideas.

Definition

Key circuit quantities

Current, $I$ , is the rate of flow of electric charge. It is measured in amperes, A.
Potential difference, $V$ , often called voltage, is the energy transferred per unit charge as charge passes through a component. It is measured in volts, V.
Resistance, $R$ , tells you how difficult it is for current to flow through a component. It is measured in ohms, Ω.

Power means energy transferred per second

Power is not the same as energy. Energy is the total amount transferred. Power tells you how quickly that energy is transferred.

Definition

Power

Power is the energy transferred per second. A power of 1 watt means 1 joule of energy is transferred every second.

The symbol for power is $P$ . It is measured in watts, W.

For Edexcel 1PH0, you need to recall and use:

\frac{E}{t}

where:

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

Key Idea

Power is a rate

A high-power device transfers energy quickly. A low-power device transfers energy more slowly, but if it is left on for a long time it can still transfer a large total amount of energy.

Example

Calculating power from energy and time

A phone charger transfers 18 000 J of energy in 30 minutes. Calculate its power.

Convert the time into seconds because the equation uses seconds: $\times 60 = 1800\ \text{s}$ .
Use power as energy transferred per second: $\frac{E}{t}$ .
Substitute the values: $\frac{18\,000\ \text{J}}{1800\ \text{s}} = 10\ \text{W}$ .
Interpret the result: the charger transfers 10 J of energy each second.

Common Mistake

Forgetting to convert time

In power calculations, time must be in seconds. If the question gives minutes or hours, convert before substituting into $\frac{E}{t}$ or $\times V \times t$ .

Electrical power from current and potential difference

In a circuit device, power depends on two things:

the current through the device
the potential difference across the device

A bigger current means more charge passes through each second. A bigger potential difference means each unit of charge transfers more energy. So increasing either current or potential difference increases the power transferred.

For Edexcel 1PH0, you need to recall and use:

\times V

where:

$P$ is electrical power in watts, W
$I$ is current in amperes, A
$V$ is potential difference in volts, V

To find the power of a real component, measure the current through it with an ammeter in series, and measure the potential difference across it with a voltmeter in parallel.

Circuit for measuring the power transferred by a lamp

Example

Finding current from power and voltage

A 24 W lamp is connected across a 12 V supply. Calculate the current through the lamp.

The power and potential difference are for the same lamp, so use $\times V$ .
Rearrange to make current the subject: $\frac{P}{V}$ .
Substitute the values: $\frac{24\ \text{W}}{12\ \text{V}} = 2.0\ \text{A}$ .
The lamp has a current of 2.0 A through it.

Common Mistake

Using the wrong voltage

Use the potential difference across the device you are calculating the power for, not automatically the total supply voltage. This matters especially in circuits with components in series.

Energy transferred by a device over time

If a device has power $P$ , then in time $t$ it transfers energy $E$ .

Because $\times V$ and $\frac{E}{t}$ , you can combine them to get:

\times V \times t

For this spec point, Edexcel says you must use this equation. That means you must be able to select it, substitute into it and rearrange it; it is not labelled as a recall-and-use equation in the extract. It is still worth learning because it comes directly from the two power equations.

In the equation:

$E$ is energy transferred in joules, J
$I$ is current in amperes, A
$V$ is potential difference in volts, V
$t$ is time in seconds, s

Example

Calculating energy transferred by a motor

A motor has a current of 2.0 A through it and a potential difference of 12 V across it. It runs for 5 minutes. Calculate the energy transferred.

Convert the time into seconds: $\times 60 = 300\ \text{s}$ .
Use the equation connecting current, potential difference and time: $\times V \times t$ .
Substitute the values: $2.0\ \text{A} \times 12\ \text{V} \times 300\ \text{s} = 7200\ \text{J}$ .
The motor transfers 7200 J, which is 7.2 kJ.

Tip

A quick units check

Watts are joules per second. So if your answer is in W, it should describe a rate of energy transfer. If your answer is in J, it should describe a total amount of energy transferred.

Electrical power and resistance

Sometimes you are given the current and resistance, but not the potential difference. In that case, use the resistance version of the power equation.

For Edexcel 1PH0, you need to recall and use:

I^2 \times R

where:

$P$ is electrical power in watts, W
$I$ is current in amperes, A
$R$ is resistance in ohms, Ω

This equation comes from combining $\times V$ with $\times R$ . You do not need to prove it in detail, but you should understand the idea: resistance affects the potential difference needed for a particular current, so it affects the power transferred.

Example

Using resistance to find power

A resistor has a resistance of 20 Ω. The current through it is 0.40 A. Calculate the power transferred by the resistor.

The question gives current and resistance, but not potential difference, so use $I^2 \times R$ .
Square the current: $A2I^2 = 0.40^2 = 0.16\ \text{A}^2$ .
Multiply by the resistance: $\times 20\ \Omega = 3.2\ \text{W}$ .
The resistor transfers energy at a rate of 3.2 W.

Common Mistake

Forgetting the square

In $I^2 \times R$ , the current is squared. If the current doubles, the power transferred in the same resistance becomes four times bigger, not just twice as big.

Choosing the right equation

A good way to choose is to look at which quantities you know and which one you need.

If you have energy and time, use $\frac{E}{t}$ .
If you have current and potential difference, use $\times V$ .
If you have current and resistance, use $I^2 \times R$ .
If you need energy transferred and have current, potential difference and time, use $\times V \times t$ .

Tip

Rearranging safely

Do the same operation to both sides. For example, from $\times V$ , divide both sides by $V$ to get $\frac{P}{V}$ .

What power tells you physically

A power rating tells you how quickly a device transfers energy under its normal operating conditions. For example, a 100 W heater transfers 100 J of energy every second when it is working as intended.

A more powerful device is not necessarily “better”; it just transfers energy faster. Whether that is useful depends on the purpose of the device.

Common Mistake

Power ratings depend on conditions

The power written on a device usually assumes it is connected to its correct potential difference. If the potential difference changes, the current and power may also change.

Exam technique

In the exam

Check that time is in seconds before using any equation involving power or energy.
Match the values to the same component: current through it, potential difference across it, resistance of it.
Write the equation, substitute with units, then check whether the answer should be in W or J.

Self review

Check yourself

A device transfers 600 J in 20 s. What is its power?
Why does increasing either current or potential difference increase electrical power?
A 5 Ω resistor has a current of 3 A through it. Which power equation would you use?

Electrical power

What you'll learn

What electrical power means: the energy transferred each second by a circuit device.
How electric current (flow of charge) and potential difference (energy transferred per unit charge) affect power.
How to use $\frac{E}{t}$ , $\times V$ , $I^2 \times R$ , and $\times V \times t$ .
How to choose the right equation and keep units under control.

The idea: energy is transferred in circuits

A circuit device, such as a lamp, motor, heater or resistor, transfers energy. For example:

a lamp transfers energy electrically to light and thermal stores
a motor transfers energy electrically to kinetic and thermal stores
a heater transfers energy electrically to thermal stores

The symbol for energy transferred is $E$ . It is measured in joules, J.

To understand electrical power, you need three earlier circuit ideas.

Definition

Key circuit quantities

Current, $I$ , is the rate of flow of electric charge. It is measured in amperes, A.
Potential difference, $V$ , often called voltage, is the energy transferred per unit charge as charge passes through a component. It is measured in volts, V.
Resistance, $R$ , tells you how difficult it is for current to flow through a component. It is measured in ohms, Ω.

Power means energy transferred per second

Power is not the same as energy. Energy is the total amount transferred. Power tells you how quickly that energy is transferred.

Definition

Power

Power is the energy transferred per second. A power of 1 watt means 1 joule of energy is transferred every second.

The symbol for power is $P$ . It is measured in watts, W.

For Edexcel 1PH0, you need to recall and use:

\frac{E}{t}

where:

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

Key Idea

Power is a rate

A high-power device transfers energy quickly. A low-power device transfers energy more slowly, but if it is left on for a long time it can still transfer a large total amount of energy.

Example

Calculating power from energy and time

A phone charger transfers 18 000 J of energy in 30 minutes. Calculate its power.

Convert the time into seconds because the equation uses seconds: $\times 60 = 1800\ \text{s}$ .
Use power as energy transferred per second: $\frac{E}{t}$ .
Substitute the values: $\frac{18\,000\ \text{J}}{1800\ \text{s}} = 10\ \text{W}$ .
Interpret the result: the charger transfers 10 J of energy each second.

Common Mistake

Forgetting to convert time

In power calculations, time must be in seconds. If the question gives minutes or hours, convert before substituting into $\frac{E}{t}$ or $\times V \times t$ .

Electrical power from current and potential difference

In a circuit device, power depends on two things:

the current through the device
the potential difference across the device

For Edexcel 1PH0, you need to recall and use:

\times V

where:

$P$ is electrical power in watts, W
$I$ is current in amperes, A
$V$ is potential difference in volts, V

To find the power of a real component, measure the current through it with an ammeter in series, and measure the potential difference across it with a voltmeter in parallel.

Circuit for measuring the power transferred by a lamp

Example

Finding current from power and voltage

A 24 W lamp is connected across a 12 V supply. Calculate the current through the lamp.

The power and potential difference are for the same lamp, so use $\times V$ .
Rearrange to make current the subject: $\frac{P}{V}$ .
Substitute the values: $\frac{24\ \text{W}}{12\ \text{V}} = 2.0\ \text{A}$ .
The lamp has a current of 2.0 A through it.

Common Mistake

Using the wrong voltage

Use the potential difference across the device you are calculating the power for, not automatically the total supply voltage. This matters especially in circuits with components in series.

Energy transferred by a device over time

If a device has power $P$ , then in time $t$ it transfers energy $E$ .

Because $\times V$ and $\frac{E}{t}$ , you can combine them to get:

\times V \times t

In the equation:

$E$ is energy transferred in joules, J
$I$ is current in amperes, A
$V$ is potential difference in volts, V
$t$ is time in seconds, s

Example

Calculating energy transferred by a motor

A motor has a current of 2.0 A through it and a potential difference of 12 V across it. It runs for 5 minutes. Calculate the energy transferred.

Convert the time into seconds: $\times 60 = 300\ \text{s}$ .
Use the equation connecting current, potential difference and time: $\times V \times t$ .
Substitute the values: $2.0\ \text{A} \times 12\ \text{V} \times 300\ \text{s} = 7200\ \text{J}$ .
The motor transfers 7200 J, which is 7.2 kJ.

Tip

A quick units check

Watts are joules per second. So if your answer is in W, it should describe a rate of energy transfer. If your answer is in J, it should describe a total amount of energy transferred.

Electrical power and resistance

Sometimes you are given the current and resistance, but not the potential difference. In that case, use the resistance version of the power equation.

For Edexcel 1PH0, you need to recall and use:

I^2 \times R

where:

$P$ is electrical power in watts, W
$I$ is current in amperes, A
$R$ is resistance in ohms, Ω

Example

Using resistance to find power

A resistor has a resistance of 20 Ω. The current through it is 0.40 A. Calculate the power transferred by the resistor.

The question gives current and resistance, but not potential difference, so use $I^2 \times R$ .
Square the current: $A2I^2 = 0.40^2 = 0.16\ \text{A}^2$ .
Multiply by the resistance: $\times 20\ \Omega = 3.2\ \text{W}$ .
The resistor transfers energy at a rate of 3.2 W.

Common Mistake

Forgetting the square

In $I^2 \times R$ , the current is squared. If the current doubles, the power transferred in the same resistance becomes four times bigger, not just twice as big.

Choosing the right equation

A good way to choose is to look at which quantities you know and which one you need.

If you have energy and time, use $\frac{E}{t}$ .
If you have current and potential difference, use $\times V$ .
If you have current and resistance, use $I^2 \times R$ .
If you need energy transferred and have current, potential difference and time, use $\times V \times t$ .

Tip

Rearranging safely

Do the same operation to both sides. For example, from $\times V$ , divide both sides by $V$ to get $\frac{P}{V}$ .

What power tells you physically

A more powerful device is not necessarily “better”; it just transfers energy faster. Whether that is useful depends on the purpose of the device.

Common Mistake

Power ratings depend on conditions

The power written on a device usually assumes it is connected to its correct potential difference. If the potential difference changes, the current and power may also change.

Exam technique

In the exam

Check that time is in seconds before using any equation involving power or energy.
Match the values to the same component: current through it, potential difference across it, resistance of it.
Write the equation, substitute with units, then check whether the answer should be in W or J.

Self review

Check yourself

A device transfers 600 J in 20 s. What is its power?
Why does increasing either current or potential difference increase electrical power?
A 5 Ω resistor has a current of 3 A through it. Which power equation would you use?

Electrical power

What you'll learn

The idea: energy is transferred in circuits

Power means energy transferred per second

Electrical power from current and potential difference

Energy transferred by a device over time

Electrical power and resistance

Choosing the right equation

What power tells you physically

Recap questions

You've reached the end

Electrical power

What you'll learn

The idea: energy is transferred in circuits

Power means energy transferred per second

Electrical power from current and potential difference

Energy transferred by a device over time

Electrical power and resistance

Choosing the right equation

What power tells you physically

Recap questions

You've reached the end

Electrical power

What you'll learn

The idea: energy is transferred in circuits

Power means energy transferred per second

Electrical power from current and potential difference

Energy transferred by a device over time

Electrical power and resistance

Choosing the right equation

What power tells you physically

Recap questions

You've reached the end

Electrical power Revision Guide

Electrical power

What you'll learn

The idea: energy is transferred in circuits

Power means energy transferred per second

Electrical power from current and potential difference

Energy transferred by a device over time

Electrical power and resistance

Choosing the right equation

What power tells you physically

Recap questions

You've reached the end

Electrical power Revision Guide