Each short of the laser gun most favored by Rosa the Closer, the intrepid vigila

Question

Each short 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 1.55-F capacitor charged to 54.5 kV. Rosa rightly reckons that she ca 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 495, with one possessing a dielectric constant of 959. Find the electric potential energy of the original capacitor when it charged. Calculated the electric potential energy of the upgraded capacitor when it is charged.

Explanation / Answer

given that dielectric constant is k1 = 495

and second dielectric constant is k2 = 959

Capacitnace is C = 1.55 F

and potential difference is dV = 54.5 kV

Potential energy of the original capacitor is U1 = 0.5*C*V^2 = 0.5*1.55*(54.5*1000)^2 = 2.3*10^9 J

capacitance without dielectric is Co = C/k = 1.55/495 = 3.13*10^-3 F

Potentil energy of the upgraded capacitor is U2 = 0.5*k2*C*V^2 = 0.5*959*3.13*10^-3*(54.5*1000)^2 = 4.45*10^9 J

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