Electrical Power — P = IV

P = IV — electrical power equals current times voltage. Use the p=iv formula to find watts in any circuit, with the I²R heating form and a worked bulb example.

What it means

Electrical power is the rate at which a circuit converts electrical energy into something else — light, heat, motion. Voltage tells you the energy per coulomb; current tells you coulombs per second; multiply them and you get energy per second. The rearranged form $P = I^2R$ explains why power lines run at enormous voltages: for fixed delivered power, higher voltage means lower current, and resistive heating losses fall as the square of the current. That single insight shapes the entire power grid.

Variables

Assumptions

• Steady DC conditions (for AC use RMS values)
• Component is ohmic if combining with V = IR
• P is the power dissipated or delivered, not stored

Derivation

Power is energy per unit time. Each coulomb of charge dropping through voltage $V$ loses energy $QV$; with current $I = Q/t$ charges per second, the energy rate is $P = IV$. Substituting Ohm's law gives the alternate forms $P = I^2R = V^2/R$.

Worked example

Given:

• V = 120 V
• I = 0.5 A

1. Write the power formula: $P = IV$

2. Substitute: $P = 120 \times 0.5$

3. Multiply: $P = 60\ \mathrm{W}$