Question

In the circuit shown, the cell is ideal, with EMF $=15\text{V}$. Each resistance is of $3\Omega$. The potential difference across the capacitor in the steady state is -

• A. Zero
• B. $9\text{V}$
• C. $12\text{V}$
• D. $15\text{V}$

Answer 1

The correct option is C $12\text{V}$

At, $t=\infty$, in the steady state, no current flow through capacitor $C$. So, no current will pass through the right most resistor. The current flow is shown in figure.


So, the equivalent resistance,

$R_{eq}=\frac{2R\times R}{2R+R}+R$

$\Rightarrow R_{eq}=\frac{5R}{3}$

Given, $R=3\Omega$

$\Rightarrow R_{eq}=5\Omega$

So, the current passing through the cell, $i=\frac{15}{5}=3\text{A}$

Therefore, from figure,

$i_2=i\times \frac{R}{2R+R}=3\times \frac{1}{3}=1\text{A}$,

$i_1=3-1=2\text{A}$

Potential across capacitor $C$,

$V_C=V_{DF}=V_{DE}+V_{EF}$ ​

$\Rightarrow V_C=R{i}_2+R(i_1+i_2)$

$\Rightarrow V_C=3\left(1\right)+3(2+1)=12\text{V}$

Hence, option $\left(C\right)$ is the correct answer.