What is the energy stored in an inductor when the current through it is I?

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

Answer: (A)

The energy stored in an inductor comes from the magnetic field created by current, and for a given inductance it grows with the square of the current. The relationship is W = 1/2 L I^2. You can think about building up the current from zero to I: the voltage across the inductor is v = L di/dt, and the small amount of energy added as current increases by di is dW = v i dt. Substituting v and integrating with respect to current gives dW = L i di, and integrating from 0 to I yields W = (1/2) L I^2. This reflects the magnetic energy stored due to the current. The other forms mix in voltage or apply to capacitors, not inductors.