Question

Two capacitors $A$ and $B$ with capacitances $2\mu F$ and $4\mu F$ are charged to a potential difference of $50V$ and $100V$ respectively consider a wire connected to each capacitor as shown (with free ends) the upper plate of $A$ and $B$ both are positive, an uncharged $2\mu \text{C}$ capacitor $C$ with lead wires falls on the free ends to complete circuit, find how much charge that flows in the circuit?

• A. $500\mu C$
• B. $200\mu C$
• C. $100\mu C$
• D. $400\mu C$

Answer 1

The correct option is B $200\mu C$

After connecting $C$, let $q$ amount of change flows through the circuit,


Applying $KVL$ to the loop $PQRS$,

$-\left(\frac{400-q}{4}\right)+\frac{100+q}{2}-\frac{q}{2}=0$

$-400+q+200+2q-2q=0$

$q=200\mu \text{C}$

Therefore, $q=200\mu C$ charge will flow through the circuit.

Hence, option (b) is the correct answer.