A capacitor is kept connected to the battery | vedclass

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

Question

(C) When a dielectric slab is inserted into a capacitor while it remains connected to a battery, the potential difference $V$ across the plates remain

Vedclass · Accepted Answer

Work is done at the cost of the battery

Vedclass · Answer

(C) When a dielectric slab is inserted into a capacitor while it remains connected to a battery, the potential difference $V$ across the plates remains constant.Since the capacitance $C$ increases $(C = K C_0)$, the charge $Q$ on the plates increases $(Q = CV)$.The battery must supply additional charge to the capacitor to maintain the constant potential difference.The work done by the battery is $W_{battery} = \Delta Q \cdot V = (Q_{final} - Q_{initial})V$.The change in energy stored in the capacitor is $\Delta U = \frac{1}{2} C_{final} V^2 - \frac{1}{2} C_{initial} V^2 = \frac{1}{2} \Delta C V^2$.Since $W_{battery} = \Delta C V^2$, the work done by the battery is twice the increase in stored energy.The remaining half of the energy supplied by the battery is converted into the work done by the external agent inserting the slab.Thus, the work is done at the cost of the battery.

$A$ capacitor is kept connected to the battery and a dielectric slab is inserted between the plates. During this process

Similar Questions

$A$ parallel plate capacitor has a capacitance of $2\ \mu F$ with a separation of $0.4\ cm$ between the plates. If the distance between the plates is halved and the space is filled with a dielectric material of constant $K = 2.8$,the final capacitance of the capacitor will be .....$\mu F$.

$A$ capacitor of capacity $C$ is connected to a cell of $V \, \text{volt}$. Now,a dielectric slab of dielectric constant $\epsilon_r$ is inserted into it while keeping the cell connected. Then:

$A$ parallel plate capacitor is made of two square plates of side $a$,separated by a distance $d$ $(d \ll a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$,as shown in the figure. The capacitance of this capacitor is

Vedclass Test Series

Exam Paper Generator

Online Exam Module