Energy stored in an inductor of inductance L carrying current I is given by which expression?

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Multiple Choice

Energy stored in an inductor of inductance L carrying current I is given by which expression?

Energy stored in an inductor comes from the magnetic field created by the current through the coil. The power going into the inductor is P = V I, and the voltage across an inductor relates to the current by V = L di/dt (for constant inductance L). To find the stored energy, integrate the power from the moment the current is zero up to the final current I: U = ∫ V I dt = ∫ (L di/dt) I dt = ∫ L I di. Carrying out the integral from 0 to I gives U = (1/2) L I^2, assuming L is constant. This shows the energy grows with the square of the current. This is the expression that matches the correct physics. The alternative I^2/(2L) would not have the correct units and does not come from the energy integral. The expression L I lacks the needed dependence on the current squared. The form (1/2) C V^2 belongs to a capacitor, not an inductor.

Energy stored in an inductor comes from the magnetic field created by the current through the coil. The power going into the inductor is P = V I, and the voltage across an inductor relates to the current by V = L di/dt (for constant inductance L). To find the stored energy, integrate the power from the moment the current is zero up to the final current I:

U = ∫ V I dt = ∫ (L di/dt) I dt = ∫ L I di.

Carrying out the integral from 0 to I gives U = (1/2) L I^2, assuming L is constant. This shows the energy grows with the square of the current.

This is the expression that matches the correct physics. The alternative I^2/(2L) would not have the correct units and does not come from the energy integral. The expression L I lacks the needed dependence on the current squared. The form (1/2) C V^2 belongs to a capacitor, not an inductor.

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