The energy stored in the magnetic field of an inductor is U = 1/2 L I^2. If the inductance triples from 0.5 H to 1.5 H with the current held constant, by what factor does U change?

• A. It remains the same
• B. It doubles
• C. It triples
• D. It halves

Answer: (C)

Energy stored in an inductor depends on both its inductance and the current: U = 1/2 L I^2. If the current is held constant, U scales directly with L. Here L goes from 0.5 H to 1.5 H, a factor of 3. With the same current, U also increases by that same factor. A quick check: initial U = 1/2 × 0.5 × I^2 = 0.25 I^2; final U = 1/2 × 1.5 × I^2 = 0.75 I^2; the ratio is 0.75/0.25 = 3. So the energy triples.