Question

The work done in increasing the potential of a capacitor from $V$ volt to $2V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor from $2V$ volt to $4V$ volt will be

• A. $W$
• B. $2W$
• C. $4W$
• D. $8W$

Answer 1

The correct option is C $4W$

Let us try to understand this problem in two cases:
Case 1:
When the potential is changing from $V$ to $2V$
Then the work done we know is given by
$W.D_1=U_f-U_i$
$⟹W.D_1=\frac{1}{2}C(2V{)}^2-\frac{1}{2}C{V}^2$
$\therefore W.D_1=\frac{3}{2}C{V}^2$ = $W$......(i)
Case 2:
When the potential of the same capacitor further changes from $2V$ to $4V$
$W.D_2=\frac{1}{2}C(4V{)}^2-\frac{1}{2}C(2V{)}^2$
$⟹W.D_2=\frac{12}{2}C{V}^2=6C{V}^2$.......(ii)
Comparing (i) & (ii) we get
$\therefore W.D_2$ = $4W$