The figure shows two identical parallel plate | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A, C, D) Initially, when the switch $K$ is closed, both capacitors $A$ and $B$ are in parallel with the battery of voltage $V$. The total energy stor

Vedclass · Accepted Answer

When the switch is opened, total energy stored in two capacitors is $\frac{5}{3} CV^2$

Vedclass · Answer

(A, C, D) Initially, when the switch $K$ is closed, both capacitors $A$ and $B$ are in parallel with the battery of voltage $V$. The total energy stored is $U = \frac{1}{2}CV^2 + \frac{1}{2}CV^2 = CV^2$.When the switch $K$ is opened, capacitor $A$ remains connected to the battery, while capacitor $B$ is isolated. The charge on $B$ remains constant at $q_B = CV$.After inserting the dielectric $(K=3)$:For capacitor $A$: The new capacitance is $C_A' = KC = 3C$. The voltage remains $V$. The energy stored is $U_A = \frac{1}{2}C_A'V^2 = \frac{1}{2}(3C)V^2 = \frac{3}{2}CV^2$.For capacitor $B$: The charge $q_B = CV$ remains constant. The new capacitance is $C_B' = KC = 3C$. The energy stored is $U_B = \frac{q_B^2}{2C_B'} = \frac{(CV)^2}{2(3C)} = \frac{C^2V^2}{6C} = \frac{1}{6}CV^2$.The total energy stored is $U_{total} = U_A + U_B = \frac{3}{2}CV^2 + \frac{1}{6}CV^2 = \frac{9+1}{6}CV^2 = \frac{10}{6}CV^2 = \frac{5}{3}CV^2$.Thus, statements $A$, $C$, and $D$ are correct.

Similar Questions

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 ...... $J$.

Three concentric conducting spherical shells have radii $r, 2r$ and $3r$ and $Q_1, Q_2$ and $Q_3$ are final charges respectively. The innermost and outermost shells are earthed as shown in the figure. Choose the wrong statement.

$A$ capacitor $C_1 = 1\,\mu F$ can withstand a maximum voltage of $V_1 = 6\,kV$,and a capacitor $C_2 = 3\,\mu F$ can withstand a maximum voltage of $V_2 = 4\,kV$. If these two capacitors are connected in series,what is the maximum voltage (in $kV$) that can be applied to the combination?

$A$ capacitor of $2\,\mu F$ capacitance is charged steadily from $0$ to $5\,C$. Which of the following graphs correctly represents the variation of potential difference $(V)$ across its plates with respect to the charge $(Q)$ on the capacitor?

Vedclass Test Series

Exam Paper Generator

Online Exam Module