electrical power
/ ee-LEK-trik-al POW-er /
Electrical power is the rate at which electrical energy is delivered or used up, how fast a circuit turns electrical energy into light, heat, motion, or sound. A 100-watt bulb is not brighter forever because it stores more energy; it is brighter because it converts energy faster than a 40-watt bulb. It answers the everyday question behind your electricity bill: how quickly is this device consuming energy right now?
Precisely, electrical power P is the electrical energy transferred per unit time, and for a component carrying current I with a voltage V across it, P = V I, measured in watts (one watt is one joule per second). For an ordinary resistor, combining this with Ohm's law V = I R gives two more handy forms, P = I^2 R and P = V^2 / R. The first shows that heating rises with the square of the current, so doubling the current quadruples the heat, which is why high-current wires must be thick and fuses protect against overload.
You meet electrical power in every rating stamped on an appliance and in the design of the grid: power stations send energy at very high voltage precisely so the current, and hence the I^2 R losses in the transmission lines, stay small. One honest clarification for beginners: energy and power are not the same. Power is the rate; energy is power multiplied by time. Your utility bills you for energy in kilowatt-hours, a 2 kW heater run for 3 hours uses 2 x 3 = 6 kWh, not for power.
A light bulb runs at 120 V and draws 0.5 A, so its power is P = V I = 120 x 0.5 = 60 watts. Equivalently, if it behaves like a resistor, P = V^2 / R tells you it has a resistance of R = V^2 / P = 120^2 / 60 = 240 ohms.
Power is voltage times current; for a resistor it also equals I^2 R or V^2 / R.
Power (watts) is the rate of using energy; energy (joules or kilowatt-hours) is power times time. Your bill charges for energy, not power. Heating goes as I^2 R, so current matters more than you might expect.