The potential differences that must be applie | vedclass

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(C) Let $C$ be the capacitance of each capacitor. The equivalent capacitance of three capacitors in parallel combination is $C_{p} = 3C$ and in series

Vedclass · Accepted Answer

$1/3$

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(C) Let $C$ be the capacitance of each capacitor. The equivalent capacitance of three capacitors in parallel combination is $C_{p} = 3C$ and in series combination is $C_{s} = C/3$.Let $V_{p}$ be the potential difference in the parallel combination and $V_{s}$ be the potential difference in the series combination. Given that the energy stored in both cases is the same:$\frac{1}{2} C_{p} V_{p}^{2} = \frac{1}{2} C_{s} V_{s}^{2}$$\frac{V_{p}^{2}}{V_{s}^{2}} = \frac{C_{s}}{C_{p}} = \frac{C/3}{3C} = \frac{1}{9}$Taking the square root on both sides:$\frac{V_{p}}{V_{s}} = \frac{1}{3}$

The potential differences that must be applied across the parallel and series combination of $3$ identical capacitors are such that the energy stored in them becomes the same. The ratio of the potential difference in the parallel combination to the series combination is:

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