(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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As shown in the figure,the work done in moving a charge $q$ from $A$ to $B$ and from $B$ to $C$ is $2 \ J$ and $-3 \ J$ respectively. The work done in moving the charge from $C$ to $A$ will be ...... $J$.

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In the figure,a system of four capacitors connected across a $10\, V$ battery is shown. The charge that will flow from switch $S$ when it is closed is:

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For what value of $C$ in $\mu F$ in the given figure,the equivalent capacitance between $A$ and $B$ becomes independent of the number of repeating sections?

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Three capacitors $A, B$ and $C$ are connected to a battery of $25 \text{ V}$ as shown in the figure. The ratio of charges on capacitors $A, B$ and $C$ will be $-$

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An automobile spring extends by $0.2\ m$ for a load of $5000\ N$. What is the ratio of the potential energy stored in the spring when it is compressed by $0.2\ m$ to the potential energy stored in a $10\ \mu F$ capacitor at a potential difference of $10000\ V$?

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As shown in the figure,the work done in moving a charge $q$ from $A$ to $B$ and from $B$ to $C$ is $2 \ J$ and $-3 \ J$ respectively. The work done in moving the charge from $C$ to $A$ will be ...... $J$.

In the figure,a system of four capacitors connected across a $10\, V$ battery is shown. The charge that will flow from switch $S$ when it is closed is:

For what value of $C$ in $\mu F$ in the given figure,the equivalent capacitance between $A$ and $B$ becomes independent of the number of repeating sections?

Three capacitors $A, B$ and $C$ are connected to a battery of $25 \text{ V}$ as shown in the figure. The ratio of charges on capacitors $A, B$ and $C$ will be $-$

An automobile spring extends by $0.2\ m$ for a load of $5000\ N$. What is the ratio of the potential energy stored in the spring when it is compressed by $0.2\ m$ to the potential energy stored in a $10\ \mu F$ capacitor at a potential difference of $10000\ V$?

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