Electrical Energy and Power

Electrical power tells us how fast energy is being transferred in a circuit. It is calculated using P = IV (power equals current times voltage). Electrical energy is simply power multiplied by time, measured in joules or kilowatt-hours.

Electrical Power

Power is the rate at which energy is transferred (how fast energy is used).

Symbol: P
Unit: Watt (W)

$P = I \times V$

Where:

$P$ = power (W)
$I$ = current (A)
$V$ = voltage (V)

Electrical Power

P = I \times V

Power (in watts) equals current (in amperes) multiplied by voltage (in volts).

Calculating Power

A kettle draws a current of 8 A from a 230 V supply. What is its power?

$P = I \times V = 8 \times 230 = 1840 \text{ W} = 1.84 \text{ kW}$

Combining with Ohm's Law

Using $V = IR$ , we can also write:

$P = I^2 R \quad \text{or} \quad P = \frac{V^2}{R}$

Electrical Energy

Energy = power × time

$E = P \times t$

Where:

$E$ = energy (J or kWh)
$P$ = power (W or kW)
$t$ = time (s or hours)

Note

Kilowatt-hour (kWh) is the unit used by electricity companies: how many kilowatts you use for how many hours. 1 kWh = 1 kW used for 1 hour = 3,600,000 J

Calculating Energy Cost

A 2 kW heater runs for 3 hours. How many kWh does it use?

$E = P \times t = 2 \text{ kW} \times 3 \text{ h} = 6 \text{ kWh}$

Real world: LED vs. incandescent light bulb — running costs

A traditional 60 W incandescent bulb produces the same light as a 9 W LED. Over 1 000 hours: the incandescent uses 60 kWh while the LED uses only 9 kWh. At an electricity price of 30 p/kWh, the saving is (60 − 9) × 0.30 = £15.30 per bulb — the LED pays for itself in weeks and runs for years.

Real world: Electricity bill — why leaving devices on standby adds up

A television on standby typically consumes 2 W continuously. Over one year (8,760 hours): E = P × t = 0.002 kW × 8,760 h = 17.5 kWh. At 30 p/kWh, that's £5.25 per year — just for one TV on standby. Across an entire household with ten standby devices, standby power can cost over £50 per year.

Real world: Electric kettle — high power, short time

A 3 kW kettle boils 1 litre of water in about 2 minutes (0.033 h). Energy used: E = 3 × 0.033 = 0.1 kWh, costing about 3 p. Despite being one of the highest-power household appliances (3,000 W), the kettle's energy use per boil is tiny because it runs for such a short time — demonstrating how both power and time matter for energy calculations.

Tip Where do you see this in real life? Every appliance label shows its power rating in watts. Compare the energy costs of your kettle, TV, and phone charger — you might be surprised which one costs most to run!

Practice Problems

A lamp uses 2 A at 12 V. What is its power?

Show answer

P = I × V = 2 × 12 = 24 W

A 1500 W hair dryer is used for 20 minutes. How many joules of energy does it use?

Show answer

t = 20 min = 1200 s. E = P × t = 1500 × 1200 = 1,800,000 J = 1.8 MJ

A heater has resistance 50 Ω and a current of 3 A. What is its power?

Show answer

P = I² × R = 3² × 50 = 9 × 50 = 450 W