Question

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

• A. \(0.025\,J\)
• B. \(0.0125\,J\)
• C. \(0.05\,J\)
• D. \(0.1\,J\)

Hint:

Energy stored in a capacitor: \[ U=\frac{1}{2}CV^2 \] Always convert microfarads (\(\mu F\)) to farads before calculation.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The objective is to find the electrostatic potential energy stored in a capacitor given its capacitance and the voltage across it.
Step 2: Key Formula or Approach:
The energy (\(U\)) stored in a capacitor is:
\[ U = \frac{1}{2}CV^2 \]
Ensure all units are in SI (Farads and Volts).
Step 3: Detailed Explanation:
1. Convert units:
\(C = 10 \mu F = 10 \times 10^{-6} F = 10^{-5} F\).
\(V = 50 \text{ V}\).
2. Substitute into formula:
\[ U = \frac{1}{2} \times (10^{-5}) \times (50)^2 \]
\[ U = 0.5 \times 10^{-5} \times 2500 \]
\[ U = 0.5 \times 2500 \times 10^{-5} \]
\[ U = 1250 \times 10^{-5} \]
\[ U = 0.0125 \text{ J} \]
Step 4: Final Answer:
The energy stored in the capacitor is 0.0125 J.