The energy (E) stored in a capacitor is given by the formula:
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
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The energy ($E$) stored in a capacitor is given by the formula:
$$ E = \frac{1}{2} C V^2 $$
where:
$C$ is the capacitance in Farads (F)
$V$ is the voltage across the capacitor in Volts (V)
Step 1: Identify the given values.
Energy ($E$) = $8 \times 10^{-2} \text{ J}$
Voltage ($V$) = $100 \text{ V}$
Step 2: Rearrange the formula to solve for capacitance ($C$).
$$ C = \frac{2E}{V^2} $$
Step 3: Substitute the given values into the rearranged formula.
$$ C = \frac{2 \times (8 \times 10^{-2} \text{ J})}{(100 \text{ V})^2} $$
$$ C = \frac{16 \times 10^{-2}}{10000} $$
$$ C = \frac{0.16}{10000} $$
$$ C = 0.000016 \text{ F} $$
Step 4: 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 $\boxed{\text{A) } 16 \mu\text{F}}$.
What's next?
