(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 Electrostatic 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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Electrostatic Potential and Capacitance

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Mix Examples - Electric Potential and Capacitance

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Three isolated equal charges are placed at the three corners of an equilateral triangle as shown in the figure. The statement which is true for the net electric potential $V$ and net electric field intensity $E$ at the centre of the triangle is

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$n$ small drops of the same size are charged to $V$ volts each. If they coalesce to form a single large drop,then its potential will be:

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$A$ capacitor of capacitance $C$ is connected to a battery of $V$ volts. Now,the distance between the plates of the capacitor is halved while keeping the charge constant,and it is again charged to $V$ volts. What is the energy supplied by the battery?

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When a number of charged liquid drops coalesce,which of the following quantities does not change?

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$A$ series combination of $N_1$ capacitors (each of capacity $C_1$) is charged to a potential difference $3V$. Another parallel combination of $N_2$ capacitors (each of capacity $C_2$) is charged to a potential difference $V$. The total energy stored in both combinations is the same. The value of $C_1$ in terms of $C_2$ is:

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Three isolated equal charges are placed at the three corners of an equilateral triangle as shown in the figure. The statement which is true for the net electric potential $V$ and net electric field intensity $E$ at the centre of the triangle is

$n$ small drops of the same size are charged to $V$ volts each. If they coalesce to form a single large drop,then its potential will be:

$A$ capacitor of capacitance $C$ is connected to a battery of $V$ volts. Now,the distance between the plates of the capacitor is halved while keeping the charge constant,and it is again charged to $V$ volts. What is the energy supplied by the battery?

When a number of charged liquid drops coalesce,which of the following quantities does not change?

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