(B) The charge on the first capacitor is $Q_1 = C \times V = CV$.The charge on the second capacitor is $Q_2 = 2C \times 2V = 4CV$.Since they are conne

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(B) The charge on the first capacitor is $Q_1 = C \times V = CV$.The charge on the second capacitor is $Q_2 = 2C \times 2V = 4CV$.Since they are connected with opposite polarity,the net charge is $Q_{net} = |Q_2 - Q_1| = |4CV - CV| = 3CV$.The total capacitance is $C_{eq} = C + 2C = 3C$.After the parallel connection,the common potential difference is $V' = \frac{Q_{net}}{C_{eq}} = \frac{3CV}{3C} = V$.The final energy of the configuration is $U_f = \frac{1}{2} C_{eq} (V')^2 = \frac{1}{2} (3C) V^2 = \frac{3}{2} CV^2$.

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

Difficult

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and charged to a potential difference $V$. Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$. The charging batteries are then removed,and the capacitors are connected in parallel such 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

$A$ $20 \mu F$ 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 $\text{J}$)

EasyTS EAMCET 2001

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Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. On bringing them in contact,there is:

Medium

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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 capacitors $C_1$ and $C_2 = 2C_1$ are connected in a circuit with a switch $S$ between them as shown in the figure. Initially,the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state,the charge on each capacitor will be

Medium

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$A$ capacitor is charged with a battery and the energy stored is $U$. After disconnecting the battery,another capacitor of the same capacity is connected in parallel to the first capacitor. Then the energy stored in each capacitor is

MediumAIPMT 2000

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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 conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. On bringing them in contact,there is:

Two capacitors $C_1$ and $C_2 = 2C_1$ are connected in a circuit with a switch $S$ between them as shown in the figure. Initially,the switch is open and $C_1$ holds charge $Q$. The switch is closed. At steady state,the charge on each capacitor will be

$A$ capacitor is charged with a battery and the energy stored is $U$. After disconnecting the battery,another capacitor of the same capacity is connected in parallel to the first capacitor. Then the energy stored in each capacitor is

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