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Power and energy
Watts, joules and kilowatt-hours; P = E × I.
Watts, joules and kilowatt-hours; P = E × I.
Power is how fast energy is used or delivered, in watts (W). Energy is the total amount used, in joules (J), or in the units on an electricity bill, kilowatt-hours (kWh). Power is the rate; energy is power kept up for a time.
A volt is one joule of energy per coulomb of charge, and an ampere is one coulomb per second. Multiply them and the coulombs cancel, leaving joules per second: watts.
A 13.8 V radio drawing 10 A is using 13.8 × 10 = 138 W. Rearranged, I = P ÷ E: 138 W from 13.8 V means 10 A, which tells you how heavy the wiring and fuse must be.
Substituting Ohm's law into P = E × I gives two more forms. Pick whichever uses the two quantities you know.
| You know | Use | Example |
|---|---|---|
| E and I | P = E × I | 13.8 V, 10 A: 138 W |
| I and R | P = I² × R | 15 A through 0.1 Ω: 225 × 0.1 = 22.5 W |
| E and R | P = E² ÷ R | 120 V across 14.4 Ω: 14 400 ÷ 14.4 = 1000 W |
The squares matter. Double the current and the heat in a given resistance quadruples, which is why undersized power wiring gets hot so quickly and why a small drop in a power lead matters most at high current. Likewise a heater element drawing 1000 W from 120 V has a resistance of 14.4 Ω and takes about 8.3 A.
Energy is power multiplied by time. A 1000 W heater running 3 hours uses 3 kWh. Battery capacity is energy too: a 12 V, 7 Ah battery holds about 12 × 7 = 84 Wh, so a 20 W load would run it for at most 84 ÷ 20 = 4.2 hours. That is an ideal figure; real batteries deliver less, and many should not be drained fully. See Batteries and Batteries, solar and portable power.
Energy is not lost; it is converted. In a resistor it becomes heat, in a lamp light and heat, in a speaker sound, and in an antenna it is radiated as radio waves. The rating printed on a part is the most it can convert safely. A common 1/4 W resistor with 10 V across 1 kΩ dissipates 0.1 W and is fine; the same 10 V across 100 Ω dissipates 1 W and will overheat. A dummy load is simply a resistor built to turn transmitter power into heat on purpose.