A capacitor consists of two parallel plates, but one of them can move relative t

Question

A capacitor consists of two parallel plates, but one of them can move relative to the other as shown in the figure. Air fills the space between the plates, and the capacitance is 28.0 pF when the separation between plates is d = 0.550 cm.

(a) A battery with potential difference V = 9.0 V is connected to the plates. What is the charge distribution, , on the left plate?

(b) What are the capacitance, C', and charge distribution, ', when d is changed to 0.275 cm?

C'= ?

'= ?

(c) With d = 0.550 cm, the battery is disconnected from the plates. The plates are then moved so that d = 0.275 cm. What is the potential difference V', between the plates?

Explanation / Answer

(a)

Q = CV

C = A/d

combine the two eqn

Q = AV/d

= Q/A = V/d = 8.854*10-12*9 /(0.55*10-2) = 1.45*10-8 Cm-2

(b)

C' = C*d/d' = 28 * (0.550/0.275) = 56 F

' = (d/d') = 2.9*10-8 Cm-2

(c) V' = Q' / C = 2Q/C = 2V = 18 V

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