Question

The energy required to charge a \( 10\,\mu\text{F} \) capacitor to \( 100\,\text{V} \) is:

• A. 0.10 J
• B. 0.05 J
• C. $5 \times 10^{-9}$ J
• D. $10 \times 10^{-9}$ J

Hint:

Use the formula $E = \frac{1}{2} C V^2$ to quickly compute energy stored in capacitors. Always convert $\mu\text{F}$ to farads first.

Answer 1

The Correct Option is B

The energy stored in a capacitor is given by the formula:
\[ E = \frac{1}{2} C V^2 \]
Where:
\( C = 10\,\mu\text{F} = 10 \times 10^{-6}\,\text{F} \)
\( V = 100\,\text{V} \)

Substitute the values:
\[ E = \frac{1}{2} \times 10 \times 10^{-6} \times (100)^2 = \frac{1}{2} \times 10 \times 10^{-6} \times 10000 = \frac{1}{2} \times 0.1 = 0.05\,\text{J} \] So, the energy required is 0.05 J.