(C) Initial charge on the first capacitor: $q_1 = CV$. Initial charge on the second capacitor: $q_2 = (2C)(2V) = 4CV$. Since they are connected with o

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(C) Initial charge on the first capacitor: $q_1 = CV$. Initial charge on the second capacitor: $q_2 = (2C)(2V) = 4CV$. Since they are connected with opposite polarities (positive to negative),the net charge $Q_{net} = q_2 - q_1 = 4CV - CV = 3CV$. The total capacitance of the parallel combination is $C_{eq} = C + 2C = 3C$. The common potential $V_{common}$ is given by $V_{common} = \frac{Q_{net}}{C_{eq}} = \frac{3CV}{3C} = V$. The final energy $U$ of the configuration is $U = \frac{1}{2} C_{eq} V_{common}^2 = \frac{1}{2} (3C) (V)^2 = \frac{3CV^2}{2}$.

Class 12 Physics Electric Potential and Capacitance Mix Examples - Electric Potential and Capacitance

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 connected to another battery and is charged to a potential difference $2V$. The charging batteries are 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

IIT 1995 All IIT

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

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Electric Potential and Capacitance

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Mix Examples - Electric Potential and Capacitance

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The figure shows a diagonal symmetric arrangement of capacitors and a battery. Identify the correct statements.

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$A$ parallel plate capacitor of capacity $100 \mu F$ is charged by a battery of $50 \text{ V}$. The battery remains connected and if the plates of the capacitor are separated so that the distance between them becomes double the original distance,the additional energy given by the battery to the capacitor in joules is

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Two parallel plate capacitors of $8 \mu F$ each are connected in parallel to a $10 \ V$ battery. The plate separation in one of the capacitors is reduced to $40 \%$ of its initial value. The increase in the total charge stored on the capacitors is

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In the circuit shown in the figure,for section $AB$,$C_1 = 1\ \mu F$,$C_2 = 2\ \mu F$,$E = 10\ V$,and the potential difference $V_A - V_B = -10\ V$. Find the charge on capacitor $C_1$.

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The figure shows a diagonal symmetric arrangement of capacitors and a battery. Identify the correct statements.

The radii of two metallic spheres $P$ and $Q$ are $r_1$ and $r_2$ respectively. They are given the same charge. If $r_1 > r_2$,then on connecting them with a thin wire,the charge will flow

Two parallel plate capacitors of $8 \mu F$ each are connected in parallel to a $10 \ V$ battery. The plate separation in one of the capacitors is reduced to $40 \%$ of its initial value. The increase in the total charge stored on the capacitors is

In the circuit shown in the figure,for section $AB$,$C_1 = 1\ \mu F$,$C_2 = 2\ \mu F$,$E = 10\ V$,and the potential difference $V_A - V_B = -10\ V$. Find the charge on capacitor $C_1$.

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