Question

Find the energy stored in a capacitor of \(10\,\mu F\) charged to a potential of \(50\,V\).

• A. \(0.0125\,J\)
• B. \(0.025\,J\)
• C. \(0.125\,J\)
• D. \(0.25\,J\)

Hint:

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

Answer 1

The Correct Option is A

Concept: The energy stored in a capacitor is given by \[ U = \frac{1}{2}CV^2 \] where
• \(C\) = capacitance
• \(V\) = potential difference
• \(U\) = stored energy

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

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

Step 3: Simplify the expression. \[ (50)^2 = 2500 \] \[ U = \frac{1}{2} \times 10 \times 10^{-6} \times 2500 \] \[ U = 12500 \times 10^{-6} \] \[ U = 0.0125\,J \] Thus the energy stored is \[ \boxed{0.0125\,J} \]