Question

A parallel-plate vacuum capacitor has 9.00 J of energy stored in it. The separation between the plates is 3.70 mm. What is the capacitance of the capacitor?

Answer 1

To find the capacitance of the parallel-plate vacuum capacitor, you can use the formula C = Q/V. Since the energy stored in the capacitor is given, you can use the formula U = (1/2)CV^2. Substitute the given values and solve for C.

Step-by-step explanation:

To find the capacitance of the parallel-plate vacuum capacitor, we can use the formula:

C = Q/V

Where C is the capacitance, Q is the charge stored in the capacitor, and V is the potential difference between the plates.

Since the energy stored in the capacitor is given, we can use the formula:

U = (1/2)CV^2

Where U is the energy, C is the capacitance, and V is the potential difference. Substitute the given values (U = 9.00 J) into the equation and rearrange to solve for C:

9.00 J = (1/2)C(V^2)

Now, substitute the given value for V (V = 3.70 mm = 3.70 x 10^-3 m) and solve for C:

C = (2U)/(V^2)

Plug in the values of U and V to find the capacitance.