A particular parallel-plate capacitor has air (k=1) between the plates. The capa

Question

A particular parallel-plate capacitor has air (k=1) between the plates. The capacitor is charged by conncting it to a 12 V battery, 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 Uo.

A slab of dielectric material, with a dielectric constant of 4, is now inserted into the capacitor, completely filling the space between the capacitor plates.

(a) in terms of Eo, the electric field between the plates in now___________ (show work/thinking)

(b) the voltage across the plates is now _________ (show work/thinking)

(c) In terms of Uo, the energy stored in the capacitor is now __________ (show work/thinking)

(d) With the slab of dielectrics 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 work/thinking)

Explanation / Answer

(a)

when dielectric is inserted the new capacitence is

C' = kC

= 4C

charge remians same

Q' = Q

C'V' = CV

4CV' = CV

V' = V/4

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

E' = E0/4

(B)

V'=Vo/4

(c)

U0 = Q^2 / 2 C

U' = Q^2/ 2 ( 4C)

= Uo/4

(d)

U' = 4 U0

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