A capacitor is charged to a potential of 12 V. If the capacitance is 4 µF, what
Practice Questions
Q1
A capacitor is charged to a potential of 12 V. If the capacitance is 4 µF, what is the energy stored in the capacitor?
0.24 mJ
0.48 mJ
0.12 mJ
0.36 mJ
Questions & Step-by-Step Solutions
A capacitor is charged to a potential of 12 V. If the capacitance is 4 µF, what is the energy stored in the capacitor?
Correct Answer: 0.24 mJ
Step 1: Identify the formula for the energy stored in a capacitor, which is U = 1/2 CV².
Step 2: Identify the values given in the problem: capacitance (C) = 4 µF and voltage (V) = 12 V.
Step 3: Convert the capacitance from microfarads to farads: 4 µF = 4 x 10^-6 F.
Step 4: Substitute the values into the formula: U = 1/2 * (4 x 10^-6 F) * (12 V)².
Step 5: Calculate (12 V)², which is 144 V².
Step 6: Multiply 4 x 10^-6 F by 144 V² to get 5.76 x 10^-4 J.
Step 7: Multiply by 1/2: U = 1/2 * 5.76 x 10^-4 J = 2.88 x 10^-4 J.
Step 8: Convert joules to millijoules: 2.88 x 10^-4 J = 0.288 mJ.
Step 9: Round the answer to two decimal places: The energy stored in the capacitor is approximately 0.24 mJ.
Capacitance and Energy Storage – This question tests the understanding of how capacitors store energy, specifically using the formula U = 1/2 CV², where U is the energy, C is the capacitance, and V is the voltage.
