(C) The capacitor $C$ is initially charged to a potential difference $V_0$. The initial charge on the capacitor is $Q = CV_0$.When this capacitor is c

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$C\left( \frac{V_0}{V} - 1 \right)$

(C) The capacitor $C$ is initially charged to a potential difference $V_0$. The initial charge on the capacitor is $Q = CV_0$.When this capacitor is connected to an uncharged capacitor of capacitance $C_x$,the total charge $Q$ is conserved and distributed between the two capacitors.Since they are connected in parallel,they will share a common potential difference $V$.The total charge remains $Q = (C + C_x)V$.Equating the initial and final charges: $CV_0 = (C + C_x)V$.Rearranging for $C_x$: $C + C_x = \frac{CV_0}{V}$.Therefore,$C_x = C\left( \frac{V_0}{V} - 1 \right)$.

Class 12 Physics Electric Potential and Capacitance Sharing of Charge in Capacitor Circuit

Medium

$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. The charging battery is removed and the capacitor is now connected to an uncharged capacitor of unknown capacity. The potential difference across the combination becomes $V$. The unknown capacitance is

A
$C\left( \frac{V_0}{V} \right)$
B
$C\left( \frac{V_0}{V} + 1 \right)$
C
$C\left( \frac{V_0}{V} - 1 \right)$
D
$CV$

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Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

$A$ capacitor of capacitance $C$ and potential $V$ has energy $E$. It is connected to another capacitor of capacitance $2C$ and potential $2V$. Then the loss of energy is $\frac{x}{3} E$,where $x$ is . . . . . . .

DifficultJEE MAIN 2024

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Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12\, \mu C$ and $-3\, \mu C$ charges,respectively,and are at a large distance from each other. They are now connected by a conducting wire. $A$ long time after this is done,the charges on $S_{1}$ and $S_{2}$ are respectively:

DifficultJEE MAIN 2020

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Two insulated spheres of radii $R_1$ and $R_2$ having charges $Q_1$ and $Q_2$ respectively are connected to each other. There is:

Easy

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There are two conducting spheres of radii $10 \ cm$ and $20 \ cm$. One sphere is given a charge of $150 \ \mu C$ and is connected to the other sphere by a wire. What will be their common potential?

Medium

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$A$ capacitor of capacitance $10\,\mu F$ has been charged to $100\,V$. It is now connected to another uncharged capacitor in parallel. The common potential becomes $40\,V$. The capacitance of the other capacitor is......$\mu F$.

Medium

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$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. The charging battery is removed and the capacitor is now connected to an uncharged capacitor of unknown capacity. The potential difference across the combination becomes $V$. The unknown capacitance is

Similar Questions

$A$ capacitor of capacitance $C$ and potential $V$ has energy $E$. It is connected to another capacitor of capacitance $2C$ and potential $2V$. Then the loss of energy is $\frac{x}{3} E$,where $x$ is . . . . . . .

Two insulated spheres of radii $R_1$ and $R_2$ having charges $Q_1$ and $Q_2$ respectively are connected to each other. There is:

There are two conducting spheres of radii $10 \ cm$ and $20 \ cm$. One sphere is given a charge of $150 \ \mu C$ and is connected to the other sphere by a wire. What will be their common potential?

$A$ capacitor of capacitance $10\,\mu F$ has been charged to $100\,V$. It is now connected to another uncharged capacitor in parallel. The common potential becomes $40\,V$. The capacitance of the other capacitor is......$\mu F$.

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