Question

If an uncharged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is:
A. $\dfrac{1}{2}QV$
B. QV
C. $\dfrac{1}{2}Q{V^2}$
D. $Q{V^2}$

Answer 1

In order to solve this question, we need to understand the concept behind the energy stored in the capacitor. Then using the formula of the same we find the amount of loss of heat energy.

Complete step by step answer:
The capacitor contains an amount of charge that can be taken as Q.
When the amount of charge Q charge flowing through the battery, the amount of work done is W=QV
By using the formula of energy stored in capacitor is given by
=$\dfrac{1}{2}C{V^2}$
We know that $Q = CV$
Substituting the above value we get
$E = \dfrac{1}{2}QV$
Here we need to calculate the amount of heat loss
Energy lost as heat = Work done by battery − Energy stored in capacitor
Energy lost as heat =$QV - \dfrac{1}{2}QV$
Energy lost as heat =$\dfrac{1}{2}QV$.

So, the correct answer is “Option A”.

Note:
When the charge flows in the circuit there will be some amount of heat loss taking place. In some questions can be solved on the basis that when the switch is ON and OFF in the circuit then the redistribution of charge takes place and results in the occurrence of loss of heat energy exits.