(A) Initial charges on the capacitors are $Q_1 = CV$ and $Q_2 = (2C)(2V) = 4CV$.Since they are connected with opposite polarities,the net charge on th

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(A) Initial charges on the capacitors are $Q_1 = CV$ and $Q_2 = (2C)(2V) = 4CV$.Since they are connected with opposite polarities,the net charge on the system is $Q_{net} = |Q_2 - Q_1| = |4CV - CV| = 3CV$.The equivalent capacitance of the system in parallel is $C_{eq} = C + 2C = 3C$.The common potential is $V_{com} = \frac{Q_{net}}{C_{eq}} = \frac{3CV}{3C} = V$.The final energy stored in the system is $U = \frac{1}{2} C_{eq} V_{com}^2 = \frac{1}{2} (3C) (V)^2 = \frac{3}{2} CV^2$.

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

Difficult

$A$ parallel plate capacitor of capacitance $C$ is charged to a potential $V$ by a battery. Another capacitor of capacitance $2C$ is charged to a potential $2V$ by another battery. After removing the batteries,they are connected in parallel such that the positive plate of one is connected to the negative plate of the other. Calculate the final energy of the system.

A
$3/2 \ CV^2$
B
$5/2 \ CV^2$
C
$7/3 \ CV^2$
D
$4/5 \ CV^2$

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Class 12 Questions

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Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

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 $50 \; pF$ is charged by a $100 \; V$ source. It is then connected to another uncharged identical capacitor. The electrostatic energy loss in the process is $\dots \; nJ$.

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Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $-V$. These are then connected by means of a fine wire. The loss of energy will be

Difficult

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Two metal spheres have radii of $20\, cm$ and $10\, cm$ respectively, and each sphere carries a charge of $150\, \mu C$. After connecting them with a conducting wire, the common potential on them will be:

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Two metal spheres of capacitance $C_1$ and $C_2$ carry some charges. They are put in contact and then separated. The final charges $Q_1$ and $Q_2$ on them will satisfy

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?

$A$ capacitor of capacitance $50 \; pF$ is charged by a $100 \; V$ source. It is then connected to another uncharged identical capacitor. The electrostatic energy loss in the process is $\dots \; nJ$.

Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $-V$. These are then connected by means of a fine wire. The loss of energy will be

Two metal spheres have radii of $20\, cm$ and $10\, cm$ respectively, and each sphere carries a charge of $150\, \mu C$. After connecting them with a conducting wire, the common potential on them will be:

Two metal spheres of capacitance $C_1$ and $C_2$ carry some charges. They are put in contact and then separated. The final charges $Q_1$ and $Q_2$ on them will satisfy

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