Question

Find the potential difference across the capacitor, when it is fully charged. The cell has an emf of $12\text{V}$ and negligible internal resistance.

• A. $1\text{V}$
• B. $4\text{V}$
• C. $2\text{V}$
• D. zero

Answer 1

The correct option is C $2\text{V}$

In the given circuit, the capacitor is in steady state, will behave like an open switch.

$\Rightarrow R_{eq}=\frac{12\times 4}{12+4}=3\Omega$
And, $i=\frac{V}{R_{eq}}=\frac{12}{3}=4\text{Amp}$


$i_1:i_2=\frac{1}{4}:\frac{1}{12}=3:1$
And $i_1+i_2=4$
$\Rightarrow i_1=3\text{Amp}$
$i_2=1\text{Amp}$

So, $V_A=12-1\times 4=8\text{Volt}$

And, $V_B=12-3\times 2=6\text{Volt}$

$\therefore V_A-V_B=8-6=2\text{Volt}$

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