Which expression gives the energy stored in an inductor of inductance L carrying current I?

Which expression gives the energy stored in an inductor of inductance L carrying current I?

• A. U = L I
• B. U = I^2
• C. U = (1/2) L I^2
• D. U = μ0 L I^2

Answer: (C)

Energy stored in an inductor comes from the magnetic field created by the current through it. The voltage across an inductor is V = L di/dt, so the instantaneous power put into the inductor is P = VI = L i di/dt. To get the energy stored as the current rises from zero to a value I, we integrate power over time: dU = P dt = L i di. This leads to U = ∫ from 0 to I of L i di = (1/2) L I^2. The factor 1/2 appears because you’re accumulating energy as the current grows from 0 to I, and the integral of i with respect to i gives i^2/2. Thus the energy depends both on the inductance and on the square of the current. The other expressions don’t match this relationship: they either lack the necessary dependence on I^2, include irrelevant constants, or fail to produce the correct energy units.

Energy stored in an inductor comes from the magnetic field created by the current through it. The voltage across an inductor is V = L di/dt, so the instantaneous power put into the inductor is P = VI = L i di/dt. To get the energy stored as the current rises from zero to a value I, we integrate power over time: dU = P dt = L i di. This leads to U = ∫ from 0 to I of L i di = (1/2) L I^2. The factor 1/2 appears because you’re accumulating energy as the current grows from 0 to I, and the integral of i with respect to i gives i^2/2. Thus the energy depends both on the inductance and on the square of the current. The other expressions don’t match this relationship: they either lack the necessary dependence on I^2, include irrelevant constants, or fail to produce the correct energy units.