Question

Two capacitors of \( 100 \mu\text{F} \) and \( 50 \mu\text{F} \) are connected in parallel. If the potential difference across \( 100 \mu\text{F} \) is 20 V and across \( 50 \mu\text{F} \) is 40 V, then the common potential of the parallel combination will be (same polarities of the capacitor connected together)

• A. 20 V
• B. 60 V
• C. \( \frac{3}{80} \) V
• D. \( \frac{80}{3} \) V

Hint:

Charge is conserved: Total Charge $Q = Q_1 + Q_2$ before and after connection.

Answer 1

The Correct Option is D

Step 1: Formula
Common Potential $V = \frac{C_1V_1 + C_2V_2}{C_1 + C_2}$
Step 2: Calculation
$V = \frac{(100 \times 20) + (50 \times 40)}{100 + 50}$
$V = \frac{2000 + 2000}{150} = \frac{4000}{150}$
Step 3: Simplifying
$V = \frac{400}{15} = \frac{80}{3} \text{ V}$
Step 4: Conclusion
The common potential is $80/3$ V.
Final Answer:(D)