What is the capacitance of a capacitor that stores 0.01 J of energy at a voltage

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Question: What is the capacitance of a capacitor that stores 0.01 J of energy at a voltage of 10 V?

Options:

Correct Answer: 0.1 F

Solution:

Using U = 1/2 C V^2, rearranging gives C = 2U/V^2 = 2(0.01 J)/(10 V)^2 = 0.1 F.

What is the capacitance of a capacitor that stores 0.01 J of energy at a voltage of 10 V?

What is the capacitance of a capacitor that stores 0.01 J of energy at a voltage of 10 V?

Step 1: Identify the formula for the energy stored in a capacitor, which is U = 1/2 C V^2.
Step 2: Rearrange the formula to solve for capacitance (C). This gives us C = 2U / V^2.
Step 3: Substitute the given values into the formula. Here, U = 0.01 J and V = 10 V.
Step 4: Calculate V^2, which is (10 V) * (10 V) = 100 V^2.
Step 5: Now substitute U and V^2 into the rearranged formula: C = 2(0.01 J) / (100 V^2).
Step 6: Calculate the numerator: 2 * 0.01 J = 0.02 J.
Step 7: Now divide the numerator by the denominator: C = 0.02 J / 100 V^2 = 0.0002 F.
Step 8: Convert 0.0002 F to a more common unit if needed, but it is already in Farads.

Capacitance – Capacitance is the ability of a capacitor to store charge per unit voltage, calculated using the energy stored in the capacitor.
Energy in Capacitors – The energy stored in a capacitor is given by the formula U = 1/2 C V^2, where U is energy, C is capacitance, and V is voltage.