Question

A 4.95nF parallel-plate capacitor contains 28.0μJ of stored energy. What is the potential difference across the capacitor? Express your answer in volts. By how many volts would you have to increase this potential difference in order for the capacitor to store 56.0μJ of potential energy?

Answer 1

The potential difference across the capacitor is 38.1 V. To store 56.0 μJ of potential energy, the potential difference needs to be increased by 22 V.

Step-by-step explanation:

To find the potential difference across the capacitor, we can use the formula:

V = Q/C

Here, Q is the charge stored in the capacitor and C is the capacitance. We are given the capacitance as 4.95 nF and the stored energy as 28.0 μJ. Since the energy stored in a capacitor is given by the formula U = 1/2 * C * V^2, we can solve for V to find the potential difference:

V = sqrt(2 * U / C)

Substituting the given values:

V = sqrt(2 * (28.0 * 10^(-6) J) / (4.95 * 10^(-9) F)) = 38.1 V

To determine the increase in potential difference needed to store 56.0 μJ of potential energy, we can use the same formula:

V = sqrt(2 * U / C)

Substituting the new energy 56.0 μJ and the given capacitance of 4.95 nF:

V = sqrt(2 * (56.0 * 10^(-6) J) / (4.95 * 10^(-9) F)) = 60.1 V

Therefore, the potential difference needs to be increased by 60.1 - 38.1 = 22 V to store 56.0 μJ of potential energy.