Question

A capacitor of $20\mu F$ charged upto $500V$ is connected in parallel with another capacitor of $10\mu F$ which is charged upto $200V$. The common potential is

• A. 500 V
• B. 300 V
• C. 400 V
• D. 200 V

Answer 1

Answer: (C)

The common potential on the capacitor is the ratio of net charge to the net capacitance.
Common potential $(V)=\frac{\text{ Net charge }}{\text{ Net capacitance }}$
$=\frac{q_1+q_2}{C_1+C_2}$
$=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$
Herer, $C_1=20\times 10^{-6}F,$
$V_1=500V$
$C_2=10\times 10^{-6}F,$
$V_2=200V$
$\therefore V=\frac{20\times 10^{-6}\times 500+10\times 10^{-6}\times 200}{30\times 10^{-6}}$
$=400V$
When a capacitor is charged by battery, then $50\%$ of energy is liberated or wastage) as heat always.