(C) Let $n$ be the number of capacitors in each series branch and $m$ be the number of such parallel branches.For each series branch,the total potenti

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(C) Let $n$ be the number of capacitors in each series branch and $m$ be the number of such parallel branches.For each series branch,the total potential difference is $V_{total} = n \times V_{max} = n \times 500 = 3000\,V$.Thus,$n = 3000 / 500 = 6$.The equivalent capacitance of one series branch is $C_s = (1\,\mu F) / n = 1/6\,\mu F$.For $m$ such branches in parallel,the total capacitance is $C_{eq} = m \times C_s = m \times (1/6) = 2\,\mu F$.Solving for $m$,we get $m = 2 \times 6 = 12$.The total number of capacitors required is $N = n \times m = 6 \times 12 = 72$.

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

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$A$ number of capacitors,each of capacitance $1\,\mu F$ and each of which gets punctured if a potential difference exceeding $500\,V$ is applied,are provided. An arrangement suitable for giving a capacitance of $2\,\mu F$ across which $3000\,V$ may be applied requires at least:

A
$18$ component capacitors
B
$36$ component capacitors
C
$72$ component capacitors
D
$144$ component capacitors

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Class 12

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Electric Potential and Capacitance

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Equivalent Capacitance of Capacitor connected in Series and Parallel

An infinite number of identical capacitors,each of capacitance $1\,\mu F$,are connected as shown in the adjoining figure. The equivalent capacitance between $A$ and $B$ is......$\mu F$.

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The potential difference across the $4 \mu F$ capacitor in series with the parallel combination in the following circuit is: (in $V$)

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The equivalent capacitance between terminals $A$ and $B$ is:

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In the given circuit,a charge of $+80 \ \mu C$ is given to the upper plate of the $4 \ \mu F$ capacitor. Then in the steady state,the charge on the upper plate of the $3 \ \mu F$ capacitor is:

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Two parallel plate capacitors are connected in series. Each capacitor has a plate area $A$ and a separation $d$ between the plates. The dielectric constants of the media between their plates are $2$ and $4$. The separation between the plates of a single air capacitor of plate area $A$ which effectively replaces the combination is:

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$A$ number of capacitors,each of capacitance $1\,\mu F$ and each of which gets punctured if a potential difference exceeding $500\,V$ is applied,are provided. An arrangement suitable for giving a capacitance of $2\,\mu F$ across which $3000\,V$ may be applied requires at least:

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An infinite number of identical capacitors,each of capacitance $1\,\mu F$,are connected as shown in the adjoining figure. The equivalent capacitance between $A$ and $B$ is......$\mu F$.

The potential difference across the $4 \mu F$ capacitor in series with the parallel combination in the following circuit is: (in $V$)

The equivalent capacitance between terminals $A$ and $B$ is:

In the given circuit,a charge of $+80 \ \mu C$ is given to the upper plate of the $4 \ \mu F$ capacitor. Then in the steady state,the charge on the upper plate of the $3 \ \mu F$ capacitor is:

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