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

To solve the problem of finding the common potential when two capacitors are connected in parallel with opposite polarity, we will follow these steps: 

1. Calculate the initial charge on both capacitors:
   • The charge on the first capacitor, \( C_1 = C \), charged to a potential \( V \), is given by: \(Q_1 = C \times V\)
   • The charge on the second capacitor, \( C_2 = 2C \), charged to a potential \( 2V \), is given by: \(Q_2 = 2C \times 2V = 4CV\)
2. Determine the net charge when connected with opposite polarity:
   • Because they are connected with opposite polarity, the charges subtract: \(Q_{\text{net}} = -(C \times V) + 4CV = 3CV\)
3. Compute the total capacitance when the capacitors are connected in parallel:
   • The total capacitance: \(C_{\text{total}} = C + 2C = 3C\)
4. Find the common potential:
   • The common potential \( V_{\text{common}} \) is given by: \(V_{\text{common}} = \frac{Q_{\text{net}}}{C_{\text{total}}} = \frac{3CV}{3C} = V\)

Thus, the common potential when the capacitors are connected is \(V\). Therefore, the correct answer is option \( V \) .

This solution demonstrates the conservation of charge principle in capacitors connected in parallel with opposite polarities.