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

Concept: The energy stored in a capacitor is given by the formula \[ E = \frac{1}{2}CV^2 \] where \(C\) is the capacitance and \(V\) is the potential difference across the capacitor.

Step 1: Write the given values. \[ C = 10\,\mu F = 10 \times 10^{-6} F \] \[ V = 100V \]

Step 2: Substitute in the energy formula. \[ E = \frac{1}{2}CV^2 \] \[ E = \frac{1}{2} \times (10 \times 10^{-6}) \times (100)^2 \]

Step 3: Simplify the expression. \[ E = 0.5 \times 10^{-5} \times 10000 \] \[ E = 0.05 \, J \]