Question

If at $t=0$, switch $\text{S}$ is closed, then at steady state find the net charge that flows through the given circuit as shown

• A. $500\mu \text{C}$
• B. $800\mu \text{C}$
• C. $300\mu \text{C}$
• D. $400\mu \text{C}$

Answer 1

The correct option is C $300\mu \text{C}$

Let us solve this problem using potential method, assigning potential to the known points as shown in figure.

By using Kirchhoff`s junction law, considering junction at $P$, we can get

$\Rightarrow (V_0-30)20+(V_0-0)15+(V_0-0)5=0$

$\Rightarrow 20V_0-600+15V_0+5V_0=0$

$\Rightarrow 40V_0=600$

$\therefore V_0=15\text{V}$

Whatever charge flows from battery, it will pass through capacitor $C_1$.

Therefore charge passing through $C_1$ is

$Q_1=C_{1}V=20(30-15)=300\mu \text{C}$.

So, the net charge flowing through the circuit will be,

$\therefore Q_{net}=300\mu \text{C}$

Hence, option (c) is the correct answer.