Question

A capacitor of capacitance \( 10 \, \mu\text{F} \) is charged to a potential difference of \( 100 \, \text{V} \). What is the energy stored in the capacitor?

• A. \( 0.5 \, \text{J} \)
• B. \( 5.0 \, \text{J} \)
• C. \( 50.0 \, \text{J} \)
• D. \( 0.05 \, \text{J} \)

Hint:

The energy stored in a capacitor is proportional to the square of the potential difference across it, given by \( E = \frac{1}{2} C V^2 \). This formula helps calculate the energy for any given capacitor.

Answer 1

The Correct Option is A

The energy stored in a capacitor is given by the formula: \[ E = \frac{1}{2} C V^2 \] Where: - \( C = 10 \, \mu\text{F} = 10 \times 10^{-6} \, \text{F} \) (capacitance), - \( V = 100 \, \text{V} \) (potential difference). Substitute the known values into the formula: \[ E = \frac{1}{2} \times 10 \times 10^{-6} \times (100)^2 \] \[ E = \frac{1}{2} \times 10 \times 10^{-6} \times 10000 = 0.5 \, \text{J} \] Thus, the energy stored in the capacitor is \( 0.5 \, \text{J} \).