Question

If at $t=0$ switch $\text{S}$ is closed, then at steady state find charge (in$\mu \text{C}$) across each capacitor as shown in figure.

• A. $\frac{400}{3},\frac{200}{3},150$
  
• B. $\frac{100}{3},\frac{200}{3},50$
  
• C. $\frac{500}{3},\frac{400}{3},200$
  
• D. $\frac{500}{3},\frac{200}{3},100$
  

Answer 1

The correct option is D $\frac{500}{3},\frac{200}{3},100$


We can solve this problem by using potential method, by assigning potential to known points as shown in figure.

When switch is closed:

Using Kirchoff`s junction law at junction $\text{P}$, we can write

$(V_o-40)5+10(V_0-0)+15(V_0-0)=0$

$\Rightarrow 5V_0-200+10V_0+15V_0=0$

$\Rightarrow 200=30V_0$

$\therefore V_0=\frac{20}{3}V$

Using $V_0$ we can find charge on each capacitor,

Charge on $C_1$ is:

$\Rightarrow Q_1=C_1(40-\frac{20}{3})=5\left(\frac{100}{3}\right)=\frac{500}{3}\mu \text{C}$

Similarly, for $Q_2$ and $Q_3$ as follows,

$Q_2=C_2(\frac{20}{3}-0)=10\left(\frac{20}{3}\right)=\frac{200}{3}\mu \text{C}$

$Q_3=C_3(\frac{20}{3}-0)=15\left(\frac{20}{3}\right)=100\mu \text{C}$

Hence, option (d) is the correct answer.

Why this question: To understand the application of Kirchhoff's law.