Question

Two condensers of capacities \( C \) and \( 2C \) are connected in parallel and then in series with 3rd condenser of capacity \( 3C \). The combination is charged to \( V \) volt. The charge on the condenser of capacity \( C \) is

• A. \( \frac{CV}{3} \)
• B. \( \frac{CV}{2} \)
• C. \( 2CV \)
• D. \( CV \)

Hint:

For capacitors in combination, first calculate the equivalent capacitance and then use it to find the charge on each capacitor.

Answer 1

The Correct Option is B

Step 1: Understanding the combination of capacitors.
When capacitors are connected in parallel, the total capacity is the sum of the individual capacitances. When the combination is then connected in series with a third capacitor, the total capacitance is found by: \[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1 + C_2} + \frac{1}{C_3} \] where \( C_1 = C \), \( C_2 = 2C \), and \( C_3 = 3C \).
Step 2: Finding the charge on the first capacitor.
The charge on the capacitor is given by \( Q = C_{\text{total}} \times V \). After finding \( C_{\text{total}} \), the charge on the capacitor of capacity \( C \) is \( \frac{CV}{2} \).
Step 3: Conclusion.
The correct answer is (B), \( \frac{CV}{2} \).