Question

The circuit was in the shown state for a long time. Now if the switch $S$ is closed then the net charge that flows through the switch $S$ , will be:

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

Answer 1

The correct option is C $\frac{150}{3}\mu C$

Ref. image

$Q_1=Q^{\prime }+Q-Q_1$

$Q^{\prime }=2Q_1-Q$

Equivalent capacitance /circuit

ref. image

Total charge through circuit

$Q=CV$

$=\left(3\times {10}^{-6}\times 50\right)C$

$=150\mu C$

Charge through $2\mu C$ capacitor will be$=\frac{150}{3}$

Charge through $4\mu C$ capacitor will be$=2\times \frac{150}{3}$

Charge through switch will be,

$Q^{\prime }=2Q_1-Q$

$=-\frac{150}{3}\mu C$ in the downward direction or

$=\frac{150}{3}\mu C$ in reverse direction