Power, Energy, and Efficiency in Electric Circuits
Electrical power is the rate at which a circuit uses energy, found from P = VI or P = I squared R. Energy is power times time, and efficiency is the useful output divided by the total input, times 100 percent. Learn each formula with worked examples in an electric-circuit context.
What electrical power is
Electrical power is the rate at which a circuit uses energy, measured in watts (W). In a circuit it is found from the voltage across a component and the current through it: P = VI. Using Ohm's law, this can also be written as P = I²R or P = V²/R, so you can find power from any two of voltage, current, and resistance.
Electrical energy
Power tells you the rate; energy is the total amount used over time. If a device draws power P for a time t, the energy transferred is E = P × t. With power in watts and time in seconds, energy comes out in joules; electricity bills instead use the kilowatt-hour (kWh), the energy of a 1 kW device running for one hour.
Efficiency
Efficiency compares the useful output to the total input. No real device converts every joule it draws into useful output — some is always lost, usually as heat. Efficiency is the fraction that ends up useful, written as a percentage.
Efficiency is the useful energy output divided by the total energy input.
As a formula, efficiency = (useful energy output ÷ total energy input) × 100%. A motor that draws 100 J and delivers 80 J of useful work is 80% efficient; the other 20 J is wasted as heat.
Worked example
A resistor of 10 Ω carries a current of 2 A. Its power is P = I²R = (2)² × 10 = 40 W. Left on for 30 seconds, it uses E = P × t = 40 × 30 = 1200 J of energy, nearly all released as heat.