A lamp, a toaster and a TV all turn electrical energy into other forms, at different rates. That rate is power, and for electricity it comes straight from current and voltage.
Key idea
Electric power: $$P = V\,I$$ in watts. Energy used = power × time. Power companies count energy in kilowatt-hours (kWh): 1 kWh is the energy a 1,000 W device uses in 1 hour.
Why it works
Voltage is joules per coulomb, and current is coulombs per second. Multiply them and the coulombs cancel: (J/C) × (C/s) = J/s = watts. A kilowatt-hour is a unit of energy, not power: $1\,\mathrm{kW} \times 1\,\mathrm{h} = 1{,}000\,\mathrm{J/s} \times 3{,}600\,\mathrm{s} = 3{,}600{,}000\,\mathrm{J}$.
Worked example: Power from current and voltage
A hair dryer draws 10 A from a 120 V outlet. What is its power?
- $P = V\,I = 120\,\mathrm{V} \times 10\,\mathrm{A} = 1{,}200\,\mathrm{W} = 1.2\,\mathrm{kW}$.
Answer: 1,200 W
Worked example: The cost of energy
A 1.5 kW space heater runs for 4 hours. Electricity costs 15 cents per kWh. How much energy does it use, and what does it cost?
- Energy: $1.5\,\mathrm{kW} \times 4\,\mathrm{h} = 6\,\mathrm{kWh}$.
- Cost: $6 \times 15 = 90$ cents.
Answer: 6 kWh, 90 cents
Common mistake
Mixing up kilowatts (a rate) with kilowatt-hours (an amount of energy). A 2 kW kettle uses energy at 2 kW whether it runs for a minute or an hour; the kWh you pay for depend on how long it runs. Check the units: kW × h = kWh.