Question

Two capacitors $\text{A}$ and $\text{B}$ with capacitances $3\mu \text{F}$ and $2\mu \text{F}$ are charged to a potential difference of $100\text{V}$ and $180\text{V}$ respectively. They are connected to an uncharged $2\mu \text{F}$ capacitor $C$ through a switch $S$ as shown. When the switch is pressed, the charge flown in the circuit is

• A. $180\mu \text{C}$
• B. $190\mu \text{C}$
• C. $200\mu \text{C}$
• D. $210\mu \text{C}$

Answer 1

The correct option is D $210\mu \text{C}$

The initial charge distribution on the capacitors are shown below:


After the switch is closed, let the charge flown be $Q\mu \text{C}$.

The charge distribution on the plates of all three capacitors looks like this


Using $KVL$ to the given loop,

$\Rightarrow \frac{300-Q}{3}-\frac{Q}{2}+\frac{360-Q}{2}=0$

$\Rightarrow 600-2Q-3Q+1080-3Q=0$

$\Rightarrow 8Q=1680$

$\therefore Q=210\mu \text{C}$

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