Question

A capacitor of capacitance $10$$\mu F$ is charged to a potential $50$ V with a battery. The battery is now disconnected and an additional charge $200$ $\mu$C is given to the positive plate of the capacitor. The potential difference across the capacitor will be :

• A. $50V$
• B. $80V$
• C. $100V$
• D. $60V$

Answer 1

The correct option is D $60V$

The charge present on the capacitor $=CV=500\mu C$.
See the diagram,
The electric field at point P is zero because it lies inside the conductor.
$x/\left(2{ϵ}_0\right)-(700-x)/\left(2{ϵ}_0\right)-(x-700)/\left(2{ϵ}_0\right)-(200-x)/\left(2{ϵ}_0\right)=0$
$x-200+x=0\Rightarrow x=100$
Charge on inner plate $=600\mu C$
Potential $=Q/C=60V$