contents

Physics

17.8 - Energy & Power Formulas

3 min

note 1 of 6

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 6

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 6

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 4 of 6

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 5 of 6

Formula for energy transferred from current, p.d. and time

Combining $E = P t$ and $P = I V$ gives a single equation for the energy transferred to a component.

$E = I V t$

Where:

$E$ = Energy transferred, in joules (J)
$I$ = Current, in amperes (A)
$V$ = Potential difference, in volts (V)
$t$ = Time, in seconds (s)

note 6 of 6

Worked example - Energy transferred by a motor

The motor in a battery-powered toy car is connected to a 4.5 V battery. A current of 0.60 A flows through the motor for 2.5 minutes. Calculate the energy transferred by the motor.

Step 1 - Convert the time to seconds

$t = 2.5 \times 60 = 150 s$

Step 2 - Substitute into E = IVt

$E = I V t = 0.60 \times 4.5 \times 150 = 405 J$

key terms

TermDefinition

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

end of notes

Key points to remember

Take a quiz View flashcards

17.9 - How Appliances Transfer EnergyNext up

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)

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

$t = 120 \div 60 = 2 minutes$

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

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