Question

In the given circuit, the charge on $2\mu \text{F}$ capacitor $($connected to $-ve$ terminal of $25\text{V}$ battery $)$ will be
(Initially, all capacitors are uncharged)

• A. $58\mu \text{C}$
• B. $60\mu \text{C}$
• C. $48\mu \text{C}$
• D. $16\mu \text{C}$

Answer 1

The correct option is A $58\mu \text{C}$

Assuming potential $0\text{Volt}$ at the earthed point and all points on that conducting wire will have same potential.


The potential at given points as shown in figure are,

$V_A=10\text{V},V_D=30\text{V},V_C=-25\text{V}$

Applying $KCL$ at function $\text{B}$

$q_1+q_2=q_3$

$\Rightarrow C_1(10-V_B)+C_2(30-V_B)=C_3(V_B-V_C)$

The point connected with +ve terminal of battery is considered to have a high electrical potential.

$\Rightarrow 1(10-V_B)+2(30-V_B)=2(V_B-(-25)$

$\Rightarrow 10-V_B+60-2V_B=2V_B+50$

$\Rightarrow 5V_B=70-50=20$

$\therefore V_B=\frac{20}{5}=4\text{V}$

Therefore, the charge or capacitor $C_3$ is,

$q_3=C_3(V_B-V_C)=2(4-(-25\left)\right)$

$\therefore q_3=58\mu \text{C}$

Hence, option $\left(a\right)$ is correct.

$$\begin{array}{c}\text{Why this question?}\\ \text{Tip: In such problems always try to find}\\ \text{potential different across given capacitors}\\ \text{and use them while applying}\\ \text{KCL at junction.}\end{array}$$