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The energy stored in a capacitor of capacity C and potential V is given by

Asked in CBSE AIPMT 1996 · Energy stored and energy density

(1) (CV)/2
(2) (C²V²)/2
(3) (C²V)/2
(4) (CV²)/2

Answer: (4) (CV²)/2

Step-by-step solution

Charging from 0 to Q against a voltage q/C takes work ∫₀^Qq/C dq=(Q²)/(2C).

With Q=CV: U=(C²V²)/(2C).

U=(CV²)/2.

Why the other options are wrong

(1) (CV)/2 is Q/2, a charge; it is missing a factor of V.
(2) Writes (Q²)/2 with Q=CV and forgets to divide by C.
(3) No single slip gives this; C²V does not have units of energy.

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