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 1.01-F capacitor charged to 50.9 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor. This she would do by replacing the capacitor's filling, whose dielectric constant is 411, with one possessing a dielectric constant of 921. 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

given that

C = 1.01 F

V = 50.9 kV = 50900 V

part(1)

we know that potential energy of capacitor

E1 = 1/2 *C1 *V^2

E1 = 1/2 * 1.01 * (50900)^2

E1 =  1308359050 J

E1 = 13.08*10^8 J

part(2)

changing the dielectric constant changes the capacitance by that factor

C2 = C1 *(921/411) So

E2 = 1/2*C2*V^2

E2 = 1/2 * 1.01*(921/411) *(50900)^2

E2 = 29.31*10^8 J

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