College

A [tex]$25 \mu F$[/tex] capacitor is connected to a 12-volt battery. How much energy can be stored in the capacitor? ([tex]1 F=10^6 \mu F[/tex])

A. 0.00181
B. 18003
C. 0.00015
D. 150

Answer :

To find out how much energy can be stored in the capacitor, we can use the formula for the energy stored in a capacitor:

[tex]\[ E = \frac{1}{2} C V^2 \][/tex]

Where:
- [tex]\( E \)[/tex] is the energy stored in joules,
- [tex]\( C \)[/tex] is the capacitance in farads,
- [tex]\( V \)[/tex] is the voltage in volts.

Let's go through the steps:

1. Convert Capacitance to Farads:
The capacitance is given as [tex]\( 25 \, \mu F \)[/tex]. To convert microfarads ([tex]\( \mu F \)[/tex]) to farads (F), use the conversion factor [tex]\( 1 \, F = 10^6 \, \mu F \)[/tex].

[tex]\[
25 \, \mu F = 25 \times 10^{-6} \, F = 2.5 \times 10^{-5} \, F
\][/tex]

2. Calculate Energy Stored:
Now plug the capacitance in farads and the voltage (12 volts) into the energy formula:

[tex]\[
E = \frac{1}{2} \times 2.5 \times 10^{-5} \, F \times (12 \, V)^2
\][/tex]

Calculate the voltage squared:

[tex]\[
12^2 = 144
\][/tex]

Then calculate the energy stored:

[tex]\[
E = \frac{1}{2} \times 2.5 \times 10^{-5} \times 144
\][/tex]

[tex]\[
E = 0.5 \times 2.5 \times 10^{-5} \times 144
\][/tex]

[tex]\[
E = 0.0018 \, \text{joules}
\][/tex]

So, the amount of energy that can be stored in the capacitor is approximately 0.0018 joules.