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

Step 1: Understanding the Question:
The question asks to calculate the amount of electrical potential energy (\(U\)) stored in a capacitor, given its capacitance (\(C\)) and the voltage (\(V\)) across it.
Step 2: Key Formula or Approach:
The energy stored in a capacitor can be calculated using one of three equivalent formulas. The most direct one for this problem is:
\[ U = \frac{1}{2}CV^2 \] where \(U\) is energy in Joules, \(C\) is capacitance in Farads, and \(V\) is potential difference in Volts.
Step 3: Detailed Explanation:
(i) Identify and convert the given values to SI units:
- Capacitance, \(C = 10\,\mu F = 10 \times 10^{-6}\,F\).
- Potential difference, \(V = 50\,V\).
(ii) Substitute the values into the energy formula:
\[ U = \frac{1}{2} \times (10 \times 10^{-6}\,F) \times (50\,V)^2 \] \[ U = \frac{1}{2} \times 10 \times 10^{-6} \times 2500 \] (iii) Simplify the expression:
\[ U = 5 \times 10^{-6} \times 2500 \] \[ U = 12500 \times 10^{-6}\,J \] To express this in standard decimal form, move the decimal point 6 places to the left:
\[ U = 0.0125\,J \] Step 4: Final Answer:
The energy stored in the capacitor is \(0.0125\,\text{J}\).