The potential differences that must be applied across the parallel and series combination of 3 identical capacitor(C - Noon Academy

The potential differences that must be applied across the parallel and series combination of 3 identical capacitor(C

The potential differences that must be applied across the parallel and series combination of 3 identical capacitor(C

The correct option is option (C) $\frac{1}{3}$ .

Let $C$ be the capacity of each capacitor. The equivalent capacitance of three capacitors in parallel combination will be $C_{p}=3 C$ and in series combination $\mathrm{C}_{\mathrm{s}}=\frac{C}{3}$ Let $V_{P}$ be the potential difference in parallel combination and $V_{s}$ in series combination then the energy stored in the same in the two cases.
$\begin{array}{l} \therefore \frac{1}{2} C_{p} V_{p}^{2}=\frac{1}{2} C_{s} V_{s}^{2} \\ \therefore \frac{V_{p}^{2}}{V_{s}^{2}}=\frac{C_{s}}{C_{p}}=\frac{C}{3} \cdot \frac{1}{3 C}=\frac{1}{9} \\ \therefore \frac{V_{p}}{V_{s}}=\frac{1}{3} \end{array}$

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