(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 Questions

Class 12

Physics Questions

Chapter

Electric Potential and Capacitance

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Sharing of Charge in Capacitor Circuit

$A$ capacitor of capacitance $900\,\mu F$ is charged by a $100\,V$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of the uncharged capacitor is connected to the positive plate and the other plate of the uncharged capacitor is connected to the negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-2}\,J$. The value of $x$ is $..............$

MediumJEE MAIN 2023

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$A$ $2 \ \mu F$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position $2$ is (in $\%$)

IIT 2011

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Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

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$A$ capacitor of capacity $C_1$ is charged to potential $V_1$ and then disconnected. An uncharged capacitor of capacity $C_2$ is connected in parallel with $C_1$. The resultant potential $V_2$ is

EasyMHT CET 2021

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$A$ $0.2\,F$ capacitor is charged to $600\,V$ by a battery. On removing the battery,it is connected to another parallel plate capacitor of $1\,F$. The potential decreases to.........$V$.

Easy

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$A$ $2 \ \mu F$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position $2$ is (in $\%$)

Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. When they are brought into contact with each other:

$A$ capacitor of capacity $C_1$ is charged to potential $V_1$ and then disconnected. An uncharged capacitor of capacity $C_2$ is connected in parallel with $C_1$. The resultant potential $V_2$ is

$A$ $0.2\,F$ capacitor is charged to $600\,V$ by a battery. On removing the battery,it is connected to another parallel plate capacitor of $1\,F$. The potential decreases to.........$V$.

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