Question

A capacitor of \(10\,\mu F\) is charged to \(100V\). Find the energy stored in it.

• A. \(0.5 \,J\)
• B. \(0.05 \,J\)
• C. \(5 \,J\)
• D. \(0.005 \,J\)

Hint:

Energy stored in a capacitor depends on both capacitance and voltage. Use the formula \[ E=\frac{1}{2}CV^2 \] and always convert microfarads to farads before substitution.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are required to calculate the electrical potential energy stored in a capacitor when its capacitance and the potential difference across it are known.
Step 2: Key Formula or Approach:
The energy \(U\) stored in a capacitor is calculated using:
\[ U = \frac{1}{2}CV^2 \]
Step 3: Detailed Explanation:
Given values:
Capacitance, \(C = 10 \, \mu F = 10 \times 10^{-6} \, F\)
Voltage, \(V = 100 \, V\)
Plugging the values into the formula:
\[ U = \frac{1}{2} \times (10 \times 10^{-6}) \times (100)^2 \]
\[ U = \frac{1}{2} \times 10^{-5} \times 10^4 \]
\[ U = 0.5 \times 10^{-1} \]
\[ U = 0.05 \, J \]
Step 4: Final Answer:
The energy stored in the capacitor is \(0.05 \, J\).