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The energy (E) stored in a capacitor is given by the formula:

April 16, 2026Physics

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Answer

\text{A) } 16 \mu\text{F}

4 steps

The energy ( $E$ ) stored in a capacitor is given by the formula:

E = \frac{1}{2} C V^2

where:

Identify the given values.
- Energy ( $E$ ) = $8 \times 10^{-2} \text{ J}$
- Voltage ( $V$ ) = $100 \text{ V}$
Rearrange the formula to solve for capacitance ( $C$ ).
$C = \frac{2E}{V^2}$
Substitute the given values into the rearranged formula.
$C = \frac{2 \times (8 \times 10^{-2} \text{ J})}{(100 \text{ V})^2}$ $C = \frac{16 \times 10^{-2}}{10000}$ $C = \frac{0.16}{10000}$ $C = 0.000016 \text{ F}$
Convert the capacitance from Farads to microfarads ( $\mu\text{F}$ ).
Since $1 \text{ F} = 10^6 \mu\text{F}$ :
$C = 0.000016 \times 10^6 \mu\text{F}$ $C = 16 \mu\text{F}$
The final answer is $\text{A) } 16 \mu\text{F}$ .

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