Sure, let's solve the given problem step-by-step.
Question:
The energy stored in a parallel plate capacitor is 3 Joules. What is the capacitance of the capacitor if the potential difference between the plates is 220 Volts?
Given data:
1. Energy stored (E) = 3 Joules
2. Potential difference (V) = 220 Volts
To find: Capacitance (C) in microfarads ([tex]\( \mu F \)[/tex])
Step-by-step solution:
1. Write down the formula for the energy stored in a capacitor:
[tex]\[
E = \frac{1}{2} C V^2
\][/tex]
2. Rearrange the formula to solve for capacitance (C):
[tex]\[
C = \frac{2E}{V^2}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
C = \frac{2 \times 3}{220^2}
\][/tex]
4. Calculate the capacitance in Farads:
[tex]\[
C = \frac{6}{48400} \approx 0.00012396694214876034 \, \text{Farads}
\][/tex]
5. Convert the capacitance from Farads to microfarads:
[tex]\[
1 \, \text{Farad} = 10^6 \, \mu \text{Farads}
\][/tex]
[tex]\[
C \approx 0.00012396694214876034 \, \text{Farads} \times 10^6 \approx 123.96694214876034 \, \mu \text{Farads}
\][/tex]
Result:
The capacitance of the capacitor is approximately [tex]\( 124 \, \mu F \)[/tex].
So, the correct answer is:
A. [tex]\( 124 \, \mu \text{F} \)[/tex]
