Question

Two capacitors \( C \) and \( 2C \) charged to \( V \) and \( 2V \) respectively are connected in parallel with opposite polarity. The common potential is:

• A. \( V \)
• B. \( \dfrac{V}{2} \)
• C. \( \dfrac{V}{3} \)
• D. \( 3V \)

Hint:

When charged capacitors are connected in parallel, total charge is conserved. If the polarities are opposite, subtract the charges before dividing by total capacitance.

Answer 1

The Correct Option is A

Step 1: Find the initial charges on the capacitors. \[ Q_1 = C \cdot V = CV, \quad Q_2 = 2C \cdot 2V = 4CV \]
Step 2: Since the capacitors are connected with opposite polarity, the net charge is: \[ Q_{\text{net}} = 4CV - CV = 3CV \]
Step 3: The equivalent capacitance in parallel is: \[ C_{\text{eq}} = C + 2C = 3C \]
Step 4: The common potential is: \[ V_{\text{common}} = \frac{Q_{\text{net}}}{C_{\text{eq}}} = \frac{3CV}{3C} = V \]