(B) Let the initial charge on each sphere be $q$. The total charge of the system is $q + q = 2q$.When connected,the spheres reach a common potential $

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(B) Let the initial charge on each sphere be $q$. The total charge of the system is $q + q = 2q$.When connected,the spheres reach a common potential $V$. The final charges on the spheres are $q_1 = C_1 V = \frac{R_1 V}{k}$ and $q_2 = C_2 V = \frac{R_2 V}{k}$,where $k = \frac{1}{4\pi\epsilon_0}$.By the law of conservation of charge,the total initial charge equals the total final charge:$2q = q_1 + q_2$$2q = \frac{R_1 V}{k} + \frac{R_2 V}{k}$$2q = \frac{V}{k}(R_1 + R_2)$$q = \frac{V}{2k}(R_1 + R_2)$

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

Medium

Two spheres of radii $R_1$ and $R_2$ have the same initial charge $q$. They are connected by a copper wire. After they are disconnected,the potential of each sphere is $V$. What was the initial charge $q$ on each sphere?

A
$\frac{V}{k}(R_1 + R_2)$
B
$\frac{V}{2k}(R_1 + R_2)$
C
$\frac{V}{3k}(R_1 + R_2)$
D
$\frac{V}{k}\frac{R_1 R_2}{R_1 + R_2}$

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Class 12 Questions

Class 12

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Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

$A$ capacitor $C$ is fully charged with voltage $V_{0}$. After disconnecting the voltage source,it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$. The energy loss in the process after the charge is distributed between the two capacitors is $.........$ $CV_{0}^{2}$.

DifficultJEE MAIN 2020

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Using a battery,a $100 \ pF$ capacitor is charged to $60 \ V$ and then the battery is removed. After that,a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is $20 \ V$,its capacitance is: (in $pF$)

MediumJEE MAIN 2025

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$A$ capacitor of capacitance $C_{0}$ is charged to a potential $V_{0}$ and is connected with another capacitor of capacitance $C$ as shown. After closing the switch $S,$ the common potential across the two capacitors becomes $V$. The capacitance $C$ is given by

MediumWBJEE 2013

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$A$ capacitor of capacitance $C_1 = 10 \mu F$ is charged using a $9 \text{ V}$ battery. It is then removed from the battery and connected to another uncharged capacitor $C_2 = 20 \mu F$ as shown in the figure. The charge on $C_2$ after equilibrium is reached is:

MediumAP EAMCET 2022

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Choose the incorrect statement from the following: When two identical capacitors are charged individually to different potentials and connected in parallel to each other after disconnecting them from the source.

Easy

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Two spheres of radii $R_1$ and $R_2$ have the same initial charge $q$. They are connected by a copper wire. After they are disconnected,the potential of each sphere is $V$. What was the initial charge $q$ on each sphere?

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Using a battery,a $100 \ pF$ capacitor is charged to $60 \ V$ and then the battery is removed. After that,a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is $20 \ V$,its capacitance is: (in $pF$)

$A$ capacitor of capacitance $C_{0}$ is charged to a potential $V_{0}$ and is connected with another capacitor of capacitance $C$ as shown. After closing the switch $S,$ the common potential across the two capacitors becomes $V$. The capacitance $C$ is given by

$A$ capacitor of capacitance $C_1 = 10 \mu F$ is charged using a $9 \text{ V}$ battery. It is then removed from the battery and connected to another uncharged capacitor $C_2 = 20 \mu F$ as shown in the figure. The charge on $C_2$ after equilibrium is reached is:

Choose the incorrect statement from the following: When two identical capacitors are charged individually to different potentials and connected in parallel to each other after disconnecting them from the source.

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