What is the expression for the energy stored in an inductor and how does it depend on current?

• A. W = 1/2 L I^2; energy increases with current.
• B. W = L I; energy decreases with current.
• C. W = V I t; energy is independent of current.
• D. W = I^2 / (2R); energy proportional to 1/I.

Answer: (A)

Energy stored in an inductor comes from the magnetic field created by current flowing through it. The instantaneous power into the inductor is P = V I, and for an inductor V = L dI/dt. So P = L I dI/dt. If you integrate this power from zero current up to a current I, you get the stored energy W = ∫0^I L I' dI' = (1/2) L I^2. This shows the energy depends on the current squared: doubling the current makes the stored energy four times larger, and with zero current there is no stored energy. The energy also scales with inductance L—more inductance means more energy stored for the same current.

The other forms don’t match the stored magnetic energy: W = V I t would imply energy grows with time under a constant voltage, not the definite current-based storage in an ideal inductor; W = I^2/(2R) describes energy associated with a resistor’s heat loss, not stored magnetic energy.