An air-filled parallel-plate capacitor has plate areaAand plate separation d.The

Question

An air-filled parallel-plate capacitor has plate areaAand plate separation d.The capacitor is connected to a battery that creates a constantvoltage V. Find the energy U_0 stored in the capacitor. Express your answer in terms ofA,d,V,and epsilon_0. Remember to enter epsilon_0 as epsilon_0. U_0 = The capacitor is now disconnected from thebattery, and the plates of the capacitor are then slowly pulledapart until the separation reaches 3d. Find the new energy U_1 of the capacitor after this process. Express your answer in terms ofA,d,V,and epsilon_0. U_1 = The capacitor is now reconnected to thebattery, and the plate separation is restored to d. A dielectric plate is slowly moved into thecapacitor until the entire space between the plates is filled. Findthe energy U_2 of the dielectric-filled capacitor. The capacitor remainsconnected to the battery. The dielectric constant is K. Express your answer in terms ofA,d,V,K,and epsilon_0. U_2 =

Explanation / Answer

Capacitance C = 0 A/d U0 = (1/2) CV2 =(1/2)(0A/d)*V2 now d -> 3d C1 = 0 A/(3d), but the voltage isstill V, we have now: U1 = (1/2) C1 V2 =(1/2)*(0A/3d) * V2 the last case, C2 = K0A/d U2 = (1/2) C2 V2 = (1/2)(K0A/d) V2 now d -> 3d C1 = 0 A/(3d), but the voltage isstill V, we have now: U1 = (1/2) C1 V2 =(1/2)*(0A/3d) * V2 the last case, C2 = K0A/d U2 = (1/2) C2 V2 = (1/2)(K0A/d) V2

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