Question

What is the energy stored in a capacitor of capacitance \( C = 10 \, \mu\text{F} \) when a potential difference of \( V = 20 \, \text{V} \) is applied across it?

• A. \( 0.01 \, \text{J} \)
• B. \( 2 \, \text{J} \)
• C. \( 4 \, \text{J} \)
• D. \( 0.1 \, \text{J} \)

Hint:

Remember: \( \text{Energy} = \frac{1}{2} C V^2 \) for capacitors. Ensure the units of capacitance and voltage are consistent.

Answer 1

The Correct Option is A

Step 1: Use the formula for energy stored in a capacitor \[ \text{Energy} = \frac{1}{2} C V^2 \] Given: - Capacitance \( C = 10 \, \mu\text{F} = 10 \times 10^{-6} \, \text{F} \) - Voltage \( V = 20 \, \text{V} \) \[ \text{Energy} = \frac{1}{2} \times (10 \times 10^{-6}) \times (20)^2 = 0.01 \, \text{J} \] Answer: Therefore, the energy stored in the capacitor is \( 0.01 \, \text{J} \). So, the correct answer is option (1).