Electrical power: P = IV

A space heater and a desk lamp plug into the same 120 V outlet. The heater warms a whole room. The lamp lights one corner of a desk and barely warms at all. Both have 120 V across them. So voltage alone cannot be what sets how fast each one receives energy.

You've already seen power as the rate of energy transfer: a power of 1 W means 1 J transferred each second.

Here are the heater and the lamp drawn as circuits, with an ammeter in each loop.

With 120 V across it, the heater carries 12.5 A. With the same 120 V across it, the lamp carries 0.5 A.

More charge passes through the heater each second, and every coulomb transfers energy as it passes. So at the same voltage, a bigger current means more energy transferred each second: more power.

Now hold the current the same and change the voltage. A flashlight bulb carries 0.4 A with 3 V across it. A car's marker light also carries 0.4 A, but with 12 V across it.

Each coulomb through the marker light transfers 12 J instead of 3 J. So at the same current, a bigger voltage means more power.

P is the power, in watts (W). I is the current through the component, in amperes (A). V is the voltage across the component, in volts (V).

Power is measured in watts: a current of 1 A driven by a voltage of 1 V delivers a power of 1 W.

Back at the outlet, the equation settles the opening puzzle. For the heater: 12.5 A × 120 V = 1500 W, so 1500 J arrive each second. For the lamp: 0.5 A × 120 V = 60 W.

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