Question

A part of the circuit as shown in the figure. All the capacitors have capacitance of $2\mu F$, then charge on

• A. capacitor $C_1$ is zero
• B. capacitor $C_2$ is zero
• C. capacitor $C_3$ is zero
• D. any capacitor cannot be determined

Answer 1

The correct option is C capacitor $C_3$ is zero

Using Kirchhoff's Law, we get
$8-\frac{q_1}{C_1}-2-\frac{q_3}{C_3}-3=0$
Since, $C_1=C_3=2\mu F$
$\Rightarrow q_1+q_3=6...\left(1\right)$
Also
$8-\frac{q_1}{C_1}+\frac{q_2}{C_2}-2=0$
Since $C_1=C_2=2\mu F$
$\Rightarrow q_1-q_2=12...\left(2\right)$
Also, we observe that
$-q_1-q_2+q_3=0$
$\Rightarrow q_1+q_2=q_3...\left(3\right)$
Solving equations (1), (2) and (3) we get
$q_1=6\mu C,q_2=-6\mu C$ and $q_3=0$
Hence, the correct answer is (C).