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 1.37-F capacitor charged to 55.9 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 401, with one possessing a dielectric constant of 937. 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

C1 = 1.37 F

V1 = 55900 volts

U1 = electric potential energy = (0.5) C1 V12 = (0.5) (1.37) (55900)2 = 2.14 x 109 J

C2 = (937/401) (1.37) = 3.2 F

V2 = 55900 volts

U2 = electric potential energy = (0.5) C2 V22 = (0.5) (3.2) (55900)2 = 5 x 109 J

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