Question

Two capacitors, one 4 pF and the other 6 pF, connected in parallel, are charged by a 100 V battery. The energy stored in the capacitors is

• A. \(12 \times 10^{-8}\) J
• B. \(2.4 \times 10^{-8}\) J
• C. \(5.0 \times 10^{-8}\) J
• D. \(1.2 \times 10^{-6}\) J

Hint:

Capacitors in parallel: \(C_{eq} = C_1 + C_2\), same voltage. Energy \(= \dfrac{1}{2}C_{eq}V^2\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In parallel, \(C_{eq} = C_1 + C_2\). Energy \(= \dfrac{1}{2}C_{eq}V^2\).
Step 2: Detailed Explanation:
\(C_{eq} = 4 + 6 = 10\) pF \(= 10 \times 10^{-12}\) F
\[ E = \frac{1}{2} \times 10 \times 10^{-12} \times (100)^2 = \frac{1}{2} \times 10 \times 10^{-12} \times 10^4 = 5 \times 10^{-8} \text{ J} \]
Step 3: Final Answer:
Energy stored \(= \mathbf{5.0 \times 10^{-8}}\) J.