Topic 5 of 5

Power and energy

Power is how fast energy is used. Energy is how much is used over time, and it's what the customer pays for.

Three ways to work out power

P = V × I    P = I² × R    P = V² ÷ R

Use whichever matches the values you've been given. All three give the same answer for the same circuit.

• 230 V and 10 A: P = 230 × 10 = 2,300 W
• 5 A through 20 Ω: P = 5² × 20 = 25 × 20 = 500 W
• 230 V across 52.9 Ω: P = 230² ÷ 52.9 = 52,900 ÷ 52.9 = 1,000 W

Because P = I² × R, doubling the current through the same resistance gives four times the power.

Energy and cost

Energy (kWh) = power (kW) × time (hours)

Cost = energy (kWh) × price per kWh

Worked example

A 3 kW immersion heater runs for 2 hours. Electricity costs 25p per kWh (an example price; check the current tariff).

1. Energy: 3 kW × 2 h = 6 kWh
2. Cost: 6 × 25p = 150p = £1.50

Exam tip: power must be in kW and time in hours for kWh. A 500 W appliance for 30 minutes is 0.5 kW × 0.5 h = 0.25 kWh.

Try it: power and current calculator