Calculate Capacitor Energy: 3000.0 μF, 87.0 V & 6.53 J | Formulas & Solutions

In summary, a capacitor is made up of two metal conductors separated by an insulating foil and has a capacity of 3000.0 μF when charged to a potential difference of 87.0 V. To calculate the energy stored in the capacitor, the formula U= (1/2)C(dV^2) can be used. However, when trying to find the charge on the capacitor when the energy stored is 6.53 J, using the formula Q= C(dV) with the same potential difference will not give the correct answer. C is a constant and should be replaced with the given value of 3000.0 μF, and V will be different for the second question.
  • #1
kopinator
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1
A capacitor consists of two closely spaced metal conductors of large area, separated by a thin insulating foil. It has an electrical capacity of 3000.0 μF and is charged to a potential difference of 87.0 V. Calculate the amount of energy stored in the capacitor.

Calculate the charge on this capacitor when the electrical energy stored in the capacitor is 6.53 J.

U= (1/2)C(dV^2)
Q= C(dV)

I found the first answer but for the 2nd part with the 6.53 J, I'm not getting the right answer.
I figured I'd use U= (1/2)C(dV^2) and solve for C. Then plug C into Q= C(dV). dV is the same for both questions.

U= (1/2)C(dV^2)
2U/(dV^2)= C
C= 1.72e-3 F
Then,

Q= C(dV)= .14964 C
That's not right answer though. What am I doing wrong?
 
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  • #2
You already know C it is given by the question-> 3000.0 μF
C is a constant not V; V will be different for second question.
 
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1. How do I calculate the energy stored in a capacitor?

To calculate the energy stored in a capacitor, you can use the formula E = 1/2*C*V^2, where E is the energy in joules, C is the capacitance in farads, and V is the voltage across the capacitor in volts.

2. What is the capacitance of a 3000.0 μF capacitor?

The capacitance of a capacitor is measured in farads (F), and 1 microfarad (μF) is equal to 1/1,000,000 farads. Therefore, a 3000.0 μF capacitor has a capacitance of 0.003 farads.

3. How do I convert volts (V) to joules (J)?

Volt and joule are two different units of measurement - volts measure voltage, while joules measure energy. To convert volts to joules, you can use the formula J = V*C, where J is the energy in joules, V is the voltage in volts, and C is the capacitance in farads.

4. What is the relationship between capacitance and energy stored in a capacitor?

The energy stored in a capacitor is directly proportional to the capacitance and the square of the voltage. This means that as the capacitance or voltage increases, the energy stored in the capacitor also increases.

5. Can I use different units for capacitance, voltage, and energy?

Yes, you can use different units for capacitance, voltage, and energy, as long as they are consistent. For example, if the capacitance is given in microfarads, the voltage should be in volts, and the energy will be in microjoules. Just make sure to use the appropriate conversion factors when necessary.

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