Question

$A10\mu \text{F}$ capacitor is fully charged to a potential difference of $50\text{V}$. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes $20\text{V}$. The capacitance of the second capacitor is

• A. $15\mu \text{F}$
• B. $30\mu \text{F}$
• C. $20\mu \text{F}$
• D. $10\mu \text{F}$

Answer 1

The correct option is A $15\mu \text{F}$

Given,
Capacitance of capacitor $C_1=10\mu \text{F}$
Potential difference before removing the source voltage,
$V_1=50\text{V}$
If $C_2$ be the capacitance of uncharged capacitor, then common potential is
$V=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$

$\Rightarrow 20=\frac{10\times 50+0}{10+C}\Rightarrow C=15\mu \text{F}$