(B) Initial charges on the capacitors are:$q_1 = C \times V = CV$$q_2 = 2C \times 2V = 4CV$When connected with opposite polarities,the net charge on t

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(B) Initial charges on the capacitors are:$q_1 = C \times V = CV$$q_2 = 2C \times 2V = 4CV$When connected with opposite polarities,the net charge on the system is:$Q_{net} = |q_2 - q_1| = |4CV - CV| = 3CV$The equivalent capacitance of the capacitors in parallel is:$C_{eq} = C + 2C = 3C$The common potential $V'$ across the combination is:$V' = \frac{Q_{net}}{C_{eq}} = \frac{3CV}{3C} = V$The final energy stored in the configuration is:$U = \frac{1}{2} C_{eq} (V')^2 = \frac{1}{2} (3C) (V)^2 = \frac{3}{2} CV^2$

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

Medium

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

A
zero
B
$\frac{3}{2} CV^2$
C
$\frac{25}{6} CV^2$
D
$\frac{9}{2} CV^2$

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Class 12

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Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

$A$ $600\,pF$ capacitor is charged by a $200\,V$ supply. It is then disconnected from the supply and connected to another uncharged $600\,pF$ capacitor. The electrostatic energy lost in the process is $.........\,\mu J$.

DifficultJEE MAIN 2023

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Two metallic spheres of radii $1 \, cm$ and $3 \, cm$ are given,with charges of $-1 \times 10^{-2} \, C$ and $5 \times 10^{-2} \, C$ respectively. If these are connected by a conducting wire,the final charge on the bigger sphere is

MediumAIPMT 2012

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In the circuit shown in the figure,initially $K_1$ is closed and $K_2$ is open. What are the charges on each capacitor? Then $K_1$ was opened and $K_2$ was closed (order is important),what will be the charge on each capacitor now? [Given: $C = 1 \,\mu F$,$C_1 = 6C$,$C_2 = 3C$,$C_3 = 3C$,$E = 9 \, V$]

Medium

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$A$ capacitor of capacitance $4 \mu F$ is charged to a potential difference of $6 \ V$ with a battery. The battery is then removed and in its place another capacitor of capacitance $8 \mu F$ is introduced and the circuit is closed. The potential difference attained by each of the capacitors in $V$ is

EasyTS EAMCET 2019

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Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

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$A$ $600\,pF$ capacitor is charged by a $200\,V$ supply. It is then disconnected from the supply and connected to another uncharged $600\,pF$ capacitor. The electrostatic energy lost in the process is $.........\,\mu J$.

Two metallic spheres of radii $1 \, cm$ and $3 \, cm$ are given,with charges of $-1 \times 10^{-2} \, C$ and $5 \times 10^{-2} \, C$ respectively. If these are connected by a conducting wire,the final charge on the bigger sphere is

Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

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