Question

In the circuit shown, capacitor is initially uncharged the switch is turned on at $t=0$. Then,

• A. At $t=0$, current supplied by battery is $4\text{mA}$
• B. At $t=0$, current in $R_3$ is $2\text{mA}$
• C. In the steady state, current supplied by battery is $3\text{mA}$
• D. In the steady state, current in $R_3$ is zero

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A At $t=0$, current supplied by battery is $4\text{mA}$
B At $t=0$, current in $R_3$ is $2\text{mA}$
C In the steady state, current supplied by battery is $3\text{mA}$
D In the steady state, current in $R_3$ is zero

At $t=0$, uncharged capacitor has zero potential difference (acts as a conducting wire).

Therefore, equivalent resistance in the circuit will be
$R_{eq}=3K\Omega$
So, current supplied by the battery,
$i_1=\frac{12\text{V}}{3\text{K}\Omega }=4\text{mA}$
The current is divided equally in parallel resistors of equal resistances, therefore
$i_2=i_3=\frac{i_1}{2}=2\text{mA}$
Now, in steady state, capacitor does not allow current flow, so

$i_1=i_2=\frac{12\text{V}}{4\text{K}\Omega }=3\text{mA}$ and $i_3=0$