The potential difference that must be applied | vedclass

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(C) Let the capacitance of each capacitor be $C$. For $4$ identical capacitors in series,the equivalent capacitance is $C_s = \frac{C}{4}$. The energy

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$4: 1$

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(C) Let the capacitance of each capacitor be $C$. For $4$ identical capacitors in series,the equivalent capacitance is $C_s = \frac{C}{4}$. The energy stored is $U_s = \frac{1}{2} C_s V_s^2 = \frac{1}{2} (\frac{C}{4}) V_s^2$. For $4$ identical capacitors in parallel,the equivalent capacitance is $C_p = 4C$. The energy stored is $U_p = \frac{1}{2} C_p V_p^2 = \frac{1}{2} (4C) V_p^2$. Given that the energy stored is the same,$U_s = U_p$: $\frac{1}{2} (\frac{C}{4}) V_s^2 = \frac{1}{2} (4C) V_p^2$ $\frac{V_s^2}{4} = 4 V_p^2$ $\frac{V_s^2}{V_p^2} = 16$ $\frac{V_s}{V_p} = 4: 1$.

The potential difference that must be applied across the series and parallel combination of $4$ identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is

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