The energy, E stored in an inductor of inductance L when current I passes through it is given by the equation

Analyze the question: You are asked for the formula that gives the energy stored in the magnetic field of an inductor carrying a current I.

Concept: When current rises in an inductor, a back e.m.f. opposes the change. The source must do work against this back e.m.f., and that work is stored as energy in the magnetic field.

Derivation:

1. The back e.m.f. is e = L(dI/dt).
2. The power delivered is P = eI = LI(dI/dt).
3. The energy is the integral of power over time: E = ∫ LI dI, with I going from 0 to I.
4. So E = L × (I²/2) = ½LI².

Check using dimensions: This is a useful way to eliminate wrong options.

• Option B (LI²) is dimensionally correct but lacks the ½ factor from integration.
• Option C (½LI) has the wrong power of I. L·I is magnetic flux linkage (in weber), not energy.
• Option D (½L²I) has the wrong power of L and I.

Only option A has the correct form, with the same structure as the capacitor energy ½CV² and kinetic energy ½mv².

Answer: Option A, E = ½LI².

Tip: Compare the analogies. Inductor energy ½LI² matches kinetic energy ½mv², where L plays the role of mass (inertia) and I the role of velocity. For a capacitor it is ½CV². The energy always has a ½ and a squared quantity.