PROBLEM 1 - 8 points A particular parallel-plate capacitor has air (K- 1) betwee

Question

PROBLEM 1 - 8 points A particular parallel-plate capacitor has air (K- 1) between the plates. The capacitor is charged by connecting it to a 12 Vbattery, and then the battery is disconnected from the capacitor. At this instant in time, the electric field between the plates is Eo, and the energy stored is U. A slab of dielectric material, with a dielectric constant of 4, in now inserted into the capacitor, completely filling the space between the capacitor plates. [2 points] (a) In terms of Eo, the electric field between the plates is now (Show your work/thinking here) 2 points] (b) The voltage across the plates is now (Show your work/thinking here) [2 points] (e) In terms of Uo, the energy stored in the capacitor is now Show your work/thinking here) 2 points] (d) With the slab of dielectric still between the plates, the capacitor is then re-connected to the 12-volt battery In terms of Uo, the energy stored in the capacitor is now Show your work/thinking here)

Explanation / Answer

(A) battery is disconnected so charge on plates will not change.

Q = C V

when dielectric is inserted.

C' = 4 C

C' V' = C V

V' = V/4

E' = V'/d and E0 = V0/d

E' = E0/4 ....Ans

(B) V = V0/ 4

(C) U0 = Q^2 / 2 C

Q is constant and C increases.

hence U = U0/4

(D) when battery is conncted then

U = 4 U0

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