Question

The charge deposited on 4 µF capacitor in the circuit is

• A. $6\times10^{-6}C$
• B. $12\times10^{-6}C$
• C. $24\times10^{-6}C$
• D. $36\times10^{-6}C$

Hint:

Charge on capacitors in series is the same; in parallel, the potential difference is the same.

Answer 1

The Correct Option is C

Step 1: Equivalent Capacitance
The 4 µF and 2 µF capacitors are in parallel, giving $4 + 2 = 6~\mu F$. This combination is in series with the 6 µF capacitor. The equivalent capacitance is $\frac{6 \times 6}{6 + 6} = 3~\mu F$.
Step 2: Total Charge
Total charge in the circuit $Q = C_{eq}V = 3~\mu F \times 12~V = 36~\mu C$.
Step 3: Branch Charge
In parallel, charge divides proportionally to capacitance. For the 4 µF branch: $Q_1 = \frac{C_1}{C_1 + C_2} \times Q = \frac{4}{4+2} \times 36 = 24~\mu C$.
Final Answer: (c)