Question

Given that potential difference across $1\mu F$ capacitor is 10 V. Then :

• A. potential difference across $4\mu F$ capacitor is 40 V
• B. potential difference across $4\mu F$ capacitor is 2.5 V
• C. potential difference across $3\mu F$ capacitor is 5 V
• D. value of E is 70 V

Answer 1

The correct option is B potential difference across $4\mu F$ capacitor is 2.5 V

Here, $C_1=1\mu F,C_2=4\mu F$ and $C_3=6||3=6+3=9\mu F$ and $V_1=10V$
In series, charge is constant so $V\propto \frac{1}{C}$
Thus, $\frac{V_2}{V_1}=\frac{C_1}{C_2}=\frac{1}{4}\Rightarrow V_2=\left(1/4\right)V_1=\left(1/4\right)\left(10\right)=2.5V$
and $\frac{V_3}{V_1}=\frac{C_1}{C_3}=\frac{1}{9}\Rightarrow V_3=\left(1/9\right)V_1=\left(1/9\right)\left(10\right)=10/9V$
As capacitor 3 and 6 are in parallel so potential of each will be equal i,e $V_3=10/9V$
Total emf is $E=V_1+V_2+V_3=10+2.5+10/9=13.6V$