(A) Let the two capacitors have capacitances $C_1$ and $C_2$.The equivalent capacitance in parallel is $C_p = C_1 + C_2$.The equivalent capacitance in

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(A) Let the two capacitors have capacitances $C_1$ and $C_2$.The equivalent capacitance in parallel is $C_p = C_1 + C_2$.The equivalent capacitance in series is $C_s = \frac{C_1 C_2}{C_1 + C_2}$.Given that $C_p = 4 C_s$,we substitute the expressions:$C_1 + C_2 = 4 \left( \frac{C_1 C_2}{C_1 + C_2} \right)$$(C_1 + C_2)^2 = 4 C_1 C_2$$C_1^2 + C_2^2 + 2 C_1 C_2 = 4 C_1 C_2$$C_1^2 + C_2^2 - 2 C_1 C_2 = 0$$(C_1 - C_2)^2 = 0$Therefore,$C_1 = C_2$.

Class 12 Physics Electrostatic Potential and Capacitance Equivalent Capacitance of Capacitor connected in Series and Parallel

Medium

The combined capacity of the parallel combination of two capacitors is four times their combined capacity when connected in series. This means that:

A
Their capacities are equal
B
Their capacities are $1\,\mu F$ and $2\,\mu F$
C
Their capacities are $0.5\,\mu F$ and $1\,\mu F$
D
Their capacities are infinite

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Electrostatic Potential and Capacitance

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Equivalent Capacitance of Capacitor connected in Series and Parallel

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DifficultJEE MAIN 2018

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DifficultMHT CET 2026

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The combined capacity of the parallel combination of two capacitors is four times their combined capacity when connected in series. This means that:

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