Question

A capacitor of $10\mu F$ charged upto 250 V is connected in parallel with another capacitor of 5aF 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 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, $C_1=10\mu F,V_1=250V,C_2=5\mu F$
$V_2=100V$
$\therefore$ $V=\frac{(10\times {10}^{-6}\times 250)+(5\times {10}^{-6}\times 100)}{(10\times {10}^{-6}+5\times {10}^{-6})}$
$\Rightarrow$ $V=\frac{3000\times {10}^{-6}}{15\times {10}^{-6}}=200V$