Question

A parallel-plate vacuum capacitor has 8.62 J of energy stored in it. The separation between the plates is 4.00 mm. What is the capacitance of the capacitor?

a) 2.15 F
b) 0.43 F
c) 8.62 F
d) 21.5 F

Answer 1

To calculate the capacitance of the capacitor, the potential difference across the plates is required along with the energy stored. With only the energy and plate separation known, the capacitance cannot be determined from the given information.

Step-by-step explanation:

The energy (U) stored in a capacitor can be calculated using the formula:

U = 1/2 * C * V^2

Where C is the capacitance and V is the potential difference across the plates.

In order to find the capacitance, we need to rearrange the formula to solve for C:

C = 2U / V^2

However, we are only given the energy stored (U = 8.62 J) and the separation distance between the plates (4.00 mm). We are not given the voltage (V), and we cannot solve for capacitance without it. Therefore, we will need additional information, such as the potential difference across the plates, to accurately calculate the capacitance of the vacuum capacitor.

Given the information provided in the question, an accurate answer cannot be determined without knowing the voltage across the capacitor plates.