Electrical Power and Energy

Power — the rate at which energy is transferred, measured in watts (W). One watt is one joule per second.

For an electrical component:

P = I V

with power in watts, current in amperes and p.d. in volts. Combining this with V = IR gives a second form that is often quicker:

P = I² R

Energy transferred:

E = I V t

or equivalently E = P t, with energy in joules and time in seconds.

Choosing the right form. If the question gives you current and p.d., use P = IV. If it gives current and resistance, use P = I²R and save yourself a step. If it gives p.d. and resistance, find the current first.

The kilowatt-hour. Electricity bills do not use joules, because a joule is far too small. The unit is the kilowatt-hour (kWh) — the energy transferred by a 1 kW appliance running for 1 hour:

energy in kWh = power in kW × time in hours

cost = energy in kWh × price per kWh

Note both conversions: watts to kilowatts, and minutes or seconds to hours. Forgetting either is the usual way to lose these marks.

Why cables get warm. Current through any resistance transfers energy to the surroundings as heat, at a rate of I²R. Because the rate depends on the square of the current, doubling the current makes a cable four times as hot. This is why high-current appliances need thick cables — a larger cross-sectional area means a lower resistance and less wasted heat.

Example: a 2.5 kW kettle running for 6 minutes uses 2.5 × 0.1 = 0.25 kWh. At 28p per kWh that is 7p. In joules it would be 2500 × 360 = 900 000 J, which is true but no use on a bill.