(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 Electric 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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Electric Potential and Capacitance

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Equivalent Capacitance of Capacitor connected in Series and Parallel

The equivalent capacitance between points $X$ and $Y$ in the given figure is . . . . . . . (in $\mu F$)

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Obtain the formula for the effective capacitance of the parallel combination of $n$ capacitors.

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Two capacitors $A$ and $B$ with capacitances $2 \mu F$ and $3 \mu F$ respectively are connected in series with a $10 \ V$ battery as shown in the figure. When the switch $S$ is closed and the two capacitors get charged fully,then:

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What is the potential difference between points $A$ and $B$ in the circuit shown (in $V$)?

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The equivalent capacitance between points $A$ and $B$ in the figure shown below is .......... $\mu F$.

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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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The equivalent capacitance between points $X$ and $Y$ in the given figure is . . . . . . . (in $\mu F$)

Obtain the formula for the effective capacitance of the parallel combination of $n$ capacitors.

Two capacitors $A$ and $B$ with capacitances $2 \mu F$ and $3 \mu F$ respectively are connected in series with a $10 \ V$ battery as shown in the figure. When the switch $S$ is closed and the two capacitors get charged fully,then:

What is the potential difference between points $A$ and $B$ in the circuit shown (in $V$)?

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