(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 Questions

Class 12

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Chapter

Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

$A$ $20 \mu F$ capacitor is charged to $5 V$ and isolated. It is then connected in parallel with an uncharged $30 \mu F$ capacitor. The decrease in the energy of the system will be (in $\text{J}$)

EasyAP EAMCET 2001

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$A$ $5\, \mu F$ capacitor is charged fully by a $220\,V$ supply. It is then disconnected from the supply and is connected in series to another uncharged $2.5\, \mu F$ capacitor. If the energy change during the charge redistribution is $\frac{ X }{100} \, J$,then the value of $X$ to the nearest integer is $.....$

MediumJEE MAIN 2020

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$A$ 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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Two identical parallel plate capacitors are connected in series to a battery of $100\,V$. $A$ dielectric slab of dielectric constant $4.0$ is inserted between the plates of the second capacitor. The potential difference across the capacitors will now be respectively:

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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$A$ $20 \mu F$ capacitor is charged to $5 V$ and isolated. It is then connected in parallel with an uncharged $30 \mu F$ capacitor. The decrease in the energy of the system will be (in $\text{J}$)

Two identical parallel plate capacitors are connected in series to a battery of $100\,V$. $A$ dielectric slab of dielectric constant $4.0$ is inserted between the plates of the second capacitor. The potential difference across the capacitors will now be respectively:

$A$ 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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