Question

A capacitor of \(10\,\mu F\) is charged to \(50\,V\). Calculate the energy stored in the capacitor.

• A. \(0.00125\,J\)
• B. \(0.0125\,J\)
• C. \(0.125\,J\)
• D. \(1.25\,J\)

Hint:

Always convert microfarads to farads before calculation: \[ 1\,\mu F = 10^{-6}F. \] Then apply the energy formula \(E=\frac{1}{2}CV^2\).

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 \(C\) = capacitance, \(V\) = potential difference across the capacitor.

Step 1: Convert capacitance into SI units. \[ C = 10\,\mu F \] \[ C = 10 \times 10^{-6} F \]

Step 2: Substitute the values into the energy formula. \[ E = \frac{1}{2}CV^2 \] \[ E = \frac{1}{2}(10 \times 10^{-6})(50)^2 \]

Step 3: Simplify the expression. \[ E = \frac{1}{2}(10 \times 10^{-6})(2500) \] \[ E = 0.5 \times 10^{-5} \times 2500 \] \[ E = 0.0125\,J \]