A series combination of 10 capacitors, each of value ' C₁ ' is charged by a source of potential difference ' 4 V '. When another parallel combination of 8 capacitors, each of value ' C₂ ' is charged by a source of potential difference ' V ', it has the same total energy stored in it as in the first combination. The value of ' C₂ ' is (a) C₁/5 (b) 8/5C₁ (c) 64/5C₁ (d) C₁/40

Answer: (a). Series: Cs = C₁/10, U₁ = 1/2₁/10(4V)² = 0.8 C₁V². Parallel: Cp = 8C₂, U₂ = 1/2(8C₂)V² = 4C₂V². U₁ = U₂ ⇒ C₂ = 0.8/4C₁ = C₁/5. So the answer is (a) C₁/5.

A series combination of 10 capacitors, each of value ' C₁ ' is… | MHT CET 2025 (22 Apr, Shift 1)

Q21MHT CET 2025 · 22 APR · SHIFT 1Medium

Combination of Capacitors

A series combination of 10 capacitors, each of value ' $C_1$ ' is charged by a source of potential difference ' 4 V '. When another parallel combination of 8 capacitors, each of value ' $C_2$ ' is charged by a source of potential difference ' V ', it has the same total energy stored in it as in the first combination. The value of ' $C_2$ ' is

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Answer: (a)

Series: $C_s = \frac{C_1}{10}$ , $U_1 = \frac{1}{2}\cdot\frac{C_1}{10}(4V)^2 = 0.8\,C_1V^2$ .
Parallel: $C_p = 8C_2$ , $U_2 = \frac{1}{2}(8C_2)V^2 = 4C_2V^2$ .
$U_1 = U_2 \Rightarrow C_2 = \frac{0.8}{4}C_1 = \frac{C_1}{5}$ .
So the answer is (a) $\frac{C_1}{5}$ .

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