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:

Capacitor energy can be found either using $E = \frac{1}{2}CV^2$ directly, or by first finding the charge using $Q = CV$ and then using $E = \frac{1}{2}QV$, both give the same result. A common mistake is forgetting to convert microfarads to farads before plugging values into the formula.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the capacitance of a capacitor and the potential difference it is charged to.
The task is to find the total electrical potential energy stored within it.
Step 2: Key Formula or Approach:
The energy (\(E\)) stored in a capacitor can be calculated using the formula:
\[ E = \frac{1}{2} C V^2 \] where \(C\) is the capacitance in Farads (F) and \(V\) is the voltage in Volts (V).
Step 3: Detailed Solution:
First, convert the given capacitance from microfarads (\(\mu F\)) to standard SI units (Farads):
\[ C = 10\,\mu F = 10 \times 10^{-6}\,F = 10^{-5}\,F \] The given voltage is:
\[ V = 50\,V \] Substitute the values into the energy equation:
\[ E = \frac{1}{2} \times (10^{-5}) \times (50)^2 \] \[ E = \frac{1}{2} \times 10^{-5} \times 2500 \] \[ E = 1250 \times 10^{-5} \] To express this in standard decimal format:
\[ E = 1250 \times 0.00001 \] \[ E = 0.0125\,J \] Step 4: Final Answer:
The energy stored in the capacitor is \(0.0125\,J\).