Each shot of the laser gun most favored by Rosa the Closer, the intrepid vigilan

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 25-F capacitor charged to 53.1 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor This she would do by replacing the capacitor's filling, whose electric constant is 401, with one possessing a dielectric constant of 963. Find the electric potential energy of the original capacitor when it is charged Calculate the electric potential energy of the upgraded capacitor when it is charged.

Explanation / Answer

Here , C = 1.25 F

voltage , V = 53.1 kV

V = 5310 V

for the original capacitor

electrical potential energy = 0.5 * C*V^2

electrical potential energy = 0.5 * 1.25 * 5310^2

electrical potential energy = 1.762 *10^7 J

the electrical potential energy of original capacitor is 1.762 *10^7 J

By changing the dielectric

capacitance , C1 = 1.25 * 963/401

C1 = 3 F

electrical potential energy = 0.5 * C1 * V^2

electrical potential energy = 0.5 * 3 * 5310^2

electrical potential energy = 4.229 *10^7 J

the electrical potential energy of the upgraded capacitor is 4.229 *10^7 J

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