contents

Physics

3.9 - Energy & Power Formulas

5 min

note 1 of 8

Energy transferred from power and time

The total energy an appliance transfers depends on its power and how long it's switched on for.
Power is the electrical energy an appliance transfers each second, measured in watts (W), where 1 W = 1 J/s.

Formula for energy transferred

$E = P t$

Where:

$E$ = Energy transferred, in joules (J)
$P$ = Power, in watts (W)
$t$ = Time, in seconds (s)

note 2 of 8

Worked example - Comparing two kettles

A 2,000 W kettle is switched on for 3 minutes. How long, in minutes, would a 3,000 W kettle take to transfer the same amount of energy?

Step 1 - Convert the time to seconds

$t = 3 \times 60 = 180 s$

Step 2 - Find the energy transferred by the 2,000 W kettle

$E = P t = 2,000 \times 180 = 360,000 J$

Step 3 - Rearrange E = Pt for the time taken by the 3,000 W kettle

$t = \frac{E}{P} = \frac{360,000}{3,000} = 120 s$

Step 4 - Convert the time back to minutes

$t = 120 \div 60 = 2 minutes$

note 3 of 8

Potential difference is energy per charge - E = QV

When charge moves through a potential difference, energy is transferred.
The potential difference across a component is the energy transferred per coulomb of charge passing through it (1 V = 1 J/C).

Formula for energy transferred

$E = Q V$

Where:

$E$ = Energy transferred, in joules (J)
$Q$ = Charge, in coulombs (C)
$V$ = Potential difference, in volts (V)

A charge Q traced round a circuit labelled charge, battery and resistors, gaining +10 V at the battery on top and losing -5 V at each of the two resistors below. — The charge gains energy at the battery and transfers it in the two resistors.

note 4 of 8

Worked example - Energy transferred by a motor

The motor in a battery-powered toy car is connected to a 6 V battery. 90 C of charge passes through the motor while the car is running. Calculate the energy transferred.

Step 1 - Identify the values

Charge: $Q = 90$ C
Potential difference: $V = 6$ V

Step 2 - Substitute into E = QV

$E = Q V = 90 \times 6 = 540 J$

note 5 of 8

Formula for electrical power

$P = I V$

Where:

$P$ = Power, in watts (W)
$I$ = Current, in amperes (A)
$V$ = Potential difference, in volts (V)

Electrical power can be found from the potential difference across an appliance and the current through it.

note 6 of 8

Worked example - Finding the current with P = IV

A 1.8 kW electric iron is connected to a 230 V supply. Calculate the current through the iron. Give your answer to two significant figures.

Step 1 - Convert the power to watts

1.8 kW = 1,800 W

Step 2 - Rearrange P = IV for the current

$I = \frac{P}{V}$

Step 3 - Substitute the values

$I = \frac{1,800}{230} = 7.82... = 7.8 A (to 2 s.f.)$

note 7 of 8

Formula for power from current and resistance

The power of a component can be found from its current and resistance by substituting $V = I R$ into $P = I V$ .

$P = I^{2} R$

Where:

$P$ = Power, in watts (W)
$I$ = Current, in amperes (A)
$R$ = Resistance, in ohms (Ω)

note 8 of 8

Worked example - Power from current and resistance

A fan heater connected to a 230 V supply has a current of 6.0 A through it. Calculate the power of the heater and its resistance. Give each answer to two significant figures.

Step 1 - Find the power with P = IV

$\begin{matrix} P & = I V \\ = 6.0 \times 230 = 1,380 \\ = 1,400 W (to 2 s.f.) \end{matrix}$

Step 2 - Rearrange P = I²R for the resistance

$\begin{matrix} R & = \frac{P}{I^{2}} \\ = \frac{1,380}{{6.0}^{2}} = \frac{1,380}{36} \\ = 38.33... = 38 Ω (to 2 s.f.) \end{matrix}$

key terms

TermDefinition

PowerThe rate at which energy is transferred or work is done.

Potential differenceThe energy transferred per coulomb of charge that moves between two points, such as across a component.

end of notes

Key points to remember

contents

Physics

3.9 - Energy & Power Formulas

5 min

note 1 of 8

Energy transferred from power and time

The total energy an appliance transfers depends on its power and how long it's switched on for.
Power is the electrical energy an appliance transfers each second, measured in watts (W), where 1 W = 1 J/s.

Formula for energy transferred

$E = P t$

Where:

$E$ = Energy transferred, in joules (J)
$P$ = Power, in watts (W)
$t$ = Time, in seconds (s)

note 2 of 8

Worked example - Comparing two kettles

A 2,000 W kettle is switched on for 3 minutes. How long, in minutes, would a 3,000 W kettle take to transfer the same amount of energy?

Step 1 - Convert the time to seconds

$t = 3 \times 60 = 180 s$

Step 2 - Find the energy transferred by the 2,000 W kettle

$E = P t = 2,000 \times 180 = 360,000 J$

Step 3 - Rearrange E = Pt for the time taken by the 3,000 W kettle

$t = \frac{E}{P} = \frac{360,000}{3,000} = 120 s$

Step 4 - Convert the time back to minutes

$t = 120 \div 60 = 2 minutes$

note 3 of 8

Potential difference is energy per charge - E = QV

When charge moves through a potential difference, energy is transferred.
The potential difference across a component is the energy transferred per coulomb of charge passing through it (1 V = 1 J/C).

Formula for energy transferred

$E = Q V$

Where:

$E$ = Energy transferred, in joules (J)
$Q$ = Charge, in coulombs (C)
$V$ = Potential difference, in volts (V)

note 4 of 8

Worked example - Energy transferred by a motor

The motor in a battery-powered toy car is connected to a 6 V battery. 90 C of charge passes through the motor while the car is running. Calculate the energy transferred.

Step 1 - Identify the values

Charge: $Q = 90$ C
Potential difference: $V = 6$ V

Step 2 - Substitute into E = QV

$E = Q V = 90 \times 6 = 540 J$

note 5 of 8

Formula for electrical power

$P = I V$

Where:

$P$ = Power, in watts (W)
$I$ = Current, in amperes (A)
$V$ = Potential difference, in volts (V)

Electrical power can be found from the potential difference across an appliance and the current through it.

note 6 of 8

Worked example - Finding the current with P = IV

A 1.8 kW electric iron is connected to a 230 V supply. Calculate the current through the iron. Give your answer to two significant figures.

Step 1 - Convert the power to watts

1.8 kW = 1,800 W

Step 2 - Rearrange P = IV for the current

$I = \frac{P}{V}$

Step 3 - Substitute the values

$I = \frac{1,800}{230} = 7.82... = 7.8 A (to 2 s.f.)$

note 7 of 8

Formula for power from current and resistance

The power of a component can be found from its current and resistance by substituting $V = I R$ into $P = I V$ .

$P = I^{2} R$

Where:

$P$ = Power, in watts (W)
$I$ = Current, in amperes (A)
$R$ = Resistance, in ohms (Ω)

note 8 of 8

Worked example - Power from current and resistance

A fan heater connected to a 230 V supply has a current of 6.0 A through it. Calculate the power of the heater and its resistance. Give each answer to two significant figures.

Step 1 - Find the power with P = IV

$\begin{matrix} P & = I V \\ = 6.0 \times 230 = 1,380 \\ = 1,400 W (to 2 s.f.) \end{matrix}$

Step 2 - Rearrange P = I²R for the resistance

$\begin{matrix} R & = \frac{P}{I^{2}} \\ = \frac{1,380}{{6.0}^{2}} = \frac{1,380}{36} \\ = 38.33... = 38 Ω (to 2 s.f.) \end{matrix}$

key terms

TermDefinition

PowerThe rate at which energy is transferred or work is done.

Potential differenceThe energy transferred per coulomb of charge that moves between two points, such as across a component.

end of notes

3.9 - Energy & Power Formulas

Energy transferred from power and time

Formula for energy transferred

Where:

Worked example - Comparing two kettles

Step 1 - Convert the time to seconds

Step 2 - Find the energy transferred by the 2,000 W kettle

Step 3 - Rearrange E = Pt for the time taken by the 3,000 W kettle

Step 4 - Convert the time back to minutes

Potential difference is energy per charge - E = QV

Formula for energy transferred

Where:

Worked example - Energy transferred by a motor

Step 1 - Identify the values

Step 2 - Substitute into E = QV

Formula for electrical power

Where:

Worked example - Finding the current with P = IV

Step 1 - Convert the power to watts

Step 2 - Rearrange P = IV for the current

Step 3 - Substitute the values

Formula for power from current and resistance

Where:

Worked example - Power from current and resistance

Step 1 - Find the power with P = IV

Step 2 - Rearrange P = I2R for the resistance

Key points to remember

3.9 - Energy & Power Formulas

Energy transferred from power and time

Formula for energy transferred

Where:

Worked example - Comparing two kettles

Step 1 - Convert the time to seconds

Step 2 - Find the energy transferred by the 2,000 W kettle

Step 3 - Rearrange E = Pt for the time taken by the 3,000 W kettle

Step 4 - Convert the time back to minutes

Potential difference is energy per charge - E = QV

Formula for energy transferred

Where:

Worked example - Energy transferred by a motor

Step 1 - Identify the values

Step 2 - Substitute into E = QV

Formula for electrical power

Where:

Worked example - Finding the current with P = IV

Step 1 - Convert the power to watts

Step 2 - Rearrange P = IV for the current

Step 3 - Substitute the values

Formula for power from current and resistance

Where:

Worked example - Power from current and resistance

Step 1 - Find the power with P = IV

Step 2 - Rearrange P = I2R for the resistance

Key points to remember

Step 2 - Rearrange P = I²R for the resistance

Step 2 - Rearrange P = I²R for the resistance