The ratio of potential difference that must be applied across parallel and series combination of two capacitors C₁ and C₂ with their capacitance in the ratio 1: 2 so that energy stored in these two cases becomes same is (a) 3: √(2) (b) √(2): 3 (c) 2: 9 (d) 9: 2

Answer: (b). Take C₁ = C, C₂ = 2C: Cp = 3C, Cs = 2C/3. Equal energy: (Vp)/(Vs) = √((Cs)/(Cp)) = √(2/3/3) = √(2/9). (Vp)/(Vs) = √(2)/3. So the answer is (b) √(2): 3.

The ratio of potential difference that must be applied across… | MHT CET 2023 (9 May, Shift 1)

Q44MHT CET 2023 · 9 MAY · SHIFT 1Medium

Combination of Capacitors

The ratio of potential difference that must be applied across parallel and series combination of two capacitors $C_1$ and $C_2$ with their capacitance in the ratio $1 : 2$ so that energy stored in these two cases becomes same is

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Answer: (b)

Take $C_1 = C$ , $C_2 = 2C$ : $C_p = 3C$ , $C_s = \frac{2C}{3}$ .
Equal energy: $\frac{V_p}{V_s} = \sqrt{\frac{C_s}{C_p}} = \sqrt{\frac{2/3}{3}} = \sqrt{\frac{2}{9}}$ .
$\frac{V_p}{V_s} = \frac{\sqrt{2}}{3}$ .
So the answer is (b) $\sqrt{2} : 3$ .

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Combination of Capacitors question from MHT CET 2023 (9 May, Shift 1)

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