The figure shows two identical parallel plate | vedclass

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

Question

(C) Initially,both capacitors $A$ and $B$ are connected in parallel to a battery of potential $V$. The capacitance of each is $C$. Total initial energ

Vedclass · Accepted Answer

$3 : 5$

Vedclass · Answer

(C) Initially,both capacitors $A$ and $B$ are connected in parallel to a battery of potential $V$. The capacitance of each is $C$. Total initial energy $U_i = \frac{1}{2}CV^2 + \frac{1}{2}CV^2 = CV^2$. When the switch $S$ is opened,capacitor $A$ remains connected to the battery,so its potential remains $V$ and its capacitance becomes $K C$. Capacitor $B$ is disconnected,so its charge $Q = CV$ remains constant,and its capacitance becomes $K C$. Final energy in capacitor $A$: $U_{Af} = \frac{1}{2}(KC)V^2 = \frac{3}{2}CV^2$. Final energy in capacitor $B$: $U_{Bf} = \frac{Q^2}{2(KC)} = \frac{(CV)^2}{2(3C)} = \frac{CV^2}{6}$. Total final energy $U_f = U_{Af} + U_{Bf} = \frac{3}{2}CV^2 + \frac{1}{6}CV^2 = \frac{9+1}{6}CV^2 = \frac{10}{6}CV^2 = \frac{5}{3}CV^2$. The ratio of initial to final energy is $\frac{U_i}{U_f} = \frac{CV^2}{(5/3)CV^2} = \frac{3}{5}$.

Similar Questions

The capacity of a parallel plate capacitor with no dielectric substance but with a separation of $0.4 \,cm$ is $2 \,\mu F$. The separation is reduced to half and it is filled with a dielectric substance of value $2.8$. The final capacity of the capacitor is.......$\mu F$.

Two parallel metal plates having charges $+Q$ and $-Q$ face each other at a certain distance between them. If the plates are now dipped in a kerosene oil tank,the electric field between the plates will

Half of the space between the plates of a parallel plate capacitor is filled with a dielectric material of dielectric constant $K$ parallel to the plates. If the initial capacitance is $C$,what will be the new (final) capacitance?

Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. $V$. If one of the capacitors is inserted in a liquid of dielectric constant $K$, then the potential difference across the other capacitor will become:

Vedclass Test Series

Exam Paper Generator

Online Exam Module