(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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Class 12 Questions

Class 12

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Chapter

Electric Potential and Capacitance

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Equivalent Capacitance of Capacitor connected in Series and Parallel

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The total capacity of the system of capacitors shown in the adjoining figure between the points $A$ and $B$ is.....$\mu F$

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In the circuit shown in the figure,the battery is $10 \ V$ and $C = 6 \ \mu F$. The charge stored in the capacitor of capacity $C$ is......$\mu C$.

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All capacitors used in the diagram are identical and each is of capacitance $C$. Then the effective capacitance between the points $A$ and $B$ is

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Four capacitors of equal capacitance have an equivalent capacitance $C_1$ when connected in series and an equivalent capacitance $C_2$ when connected in parallel. The ratio $\frac{C_1}{C_2}$ is:

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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:

Similar Questions

In the arrangement of capacitors shown in the figure,if each capacitor is $9 pF$,then the effective capacitance between the points $A$ and $B$ is (in $pF$)

The total capacity of the system of capacitors shown in the adjoining figure between the points $A$ and $B$ is.....$\mu F$

In the circuit shown in the figure,the battery is $10 \ V$ and $C = 6 \ \mu F$. The charge stored in the capacitor of capacity $C$ is......$\mu C$.

All capacitors used in the diagram are identical and each is of capacitance $C$. Then the effective capacitance between the points $A$ and $B$ is

Four capacitors of equal capacitance have an equivalent capacitance $C_1$ when connected in series and an equivalent capacitance $C_2$ when connected in parallel. The ratio $\frac{C_1}{C_2}$ is:

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