Question

A capacitor of $10\mu F$ charged upto 250 V is connected in parallel with another capacitor of $5\mu F$ charged upto 100 V. The common potential is :

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

Answer 1

Answer: (A)

The correct option is A 200 V

The equivalent capacitance of the capacitors joined in parallel is equal to the sum of their individual capacitances.

Let the charge on the capacitors be $q_1$ and $q_2.$ Then total charge

$Q=Q+Q_2$

$CV=C_1{V}_1+C_2{V}_2$

Since, capacitors are connected in parallel equivalent capacitance is $C=C_1+C_2$

$V=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$

Given, $C_1=10\mu F,V_1-250V,C_2=5\mu F,V_2=100V$

$\therefore V=\frac{(10\times {10}^{-6}\times 250)+(5\times {10}^{-6}\times 100)}{(10\times {10}^{-6}+5\times {10}^{-6})}$

$\Rightarrow V=\frac{3000\times {10}^{-6}}{15\times {10}^{-6}}=200V$