Question

Each shot of the laser gun most favored by Rosa the Closer, the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.33 F capacitor charged to 77.9 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor. She could do this by replacing the capacitor's filling, whose dielectric constant is 427, with one possessing a dielectric constant of 983.
A. Find the electric potential energy of the original capacitor when it is charged.
B. Calculate the electric potential energy of the upgraded capacitor when it is charged.

Answer 1

Answer:

A) 4.035 × 10^(9) J

B) 9.29 × 10^(9) J

Explanation:

We are given;

Capacitance of the original capacitor; C = 1.33 F

Potential difference given to the original capacitor; V = 77.9 kV = 77.9 × 10³ V

A) The formula for Potential energy (U) for the original capacitor is given as:

U = ½CV²

Plugging in the relevant values, we have;

U = ½ × 1.33 × (77.9 × 10³)²

U = 4.035 × 10^(9) J

B) We are told that the capacitor with dielectric constant of 427, was replaced with one possessing a dielectric constant of 983.

Thus;

U = ½ × 1.33 × (983/427) × (77.9 × 10³)²

U = 9.29 × 10^(9) J