CBSE Class 12 · 2024 · CapacitanceMultiple Choice

Two capacitors of capacitances

2 C_{0}

and

6 C_{0}

are first connected in series and then in parallel across the same battery. The ratio of the energy stored in the series combination to that in the parallel combination is

(A) $\frac{1}{4}$
(B) $\frac{1}{6}$
(C) $\frac{2}{15}$
(D) $\frac{3}{16}$ ✓ Correct

Answer: (D)

Solution

Across the same battery (same

V

U = \frac{1}{2} C_{e q} V^{2}

, so the energy ratio equals the capacitance ratio. Series:

C_{s} = \frac{( 2 C _{0} ) ( 6 C _{0} )}{2 C _{0} + 6 C _{0}} = \frac{12 C _{0}}{8} = 1.5 C_{0}

. Parallel:

C_{p} = 2 C_{0} + 6 C_{0} = 8 C_{0}

\frac{U _{s}}{U _{p}} = \frac{C _{s}}{C _{p}} = \frac{1.5 C _{0}}{8 C _{0}} = \frac{3}{16} .

Hence (D).

CBSE Class 12 Board · 2024 · Single correct option

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