What is the energy stored in an inductor with inductance L and current I?

• A. 1/2 L I^2
• B. L I
• C. L^2 I^2
• D. 1/2 I^2 / L

Answer: (A)

Energy stored in an inductor comes from the magnetic field created by the current, and it scales with the square of the current and the inductance. To find it, think of delivering a small amount of current di, which requires voltage v = L di/dt across the inductor. The incremental work is dW = v di. If we sweep the current from 0 to I, the total energy is W = ∫0^I v di = ∫0^I L i di = (1/2) L I^2. This shows the energy is zero when current is zero and grows with the square of the current, with L setting how much energy per unit current increases.

The expression matches units: henry times ampere squared gives joules. The other forms do not, since they mix units in ways that don’t produce energy.