So far 4 wrong answers have been tried 3.48 ,3.52, 2.48, 6.95 anybody care to se

Question

So far 4 wrong answers have been tried

3.48

,3.52,

2.48,

6.95

anybody care to see if they can solve it?

A capacitor with a 3 mm gap has a potential difference of 6 volts (see the figure). A disk of glass 2.25 mm thick, with area the same as the area of the metal plates, has a dielectric constant of 1.7. It is inserted in the middle of the gap between the metal plates. Now what is the potential difference of the two metal disks? (It helps to make a diagram showing the electric field along a path.)

Explanation / Answer

We know the formula for capacitance is Q = CV and also C = €A /D

HERE, € = pemitivity of the free space

According to the capacitor before and after placing the dielectric the charge on the capacitor remains constant due to the conservation of charges

C1 X V1 = C2 X V2

GIVEN , V1 = 6V AND d = 3mm and thickness of dielectric = 2.25mm dielectric constant (K) = 1.7 and the area of the plates are same

CAPACITANCE OF CAPACITOR WITH DIELECTRIC = €A/D - T(1 - 1/K)

So

(€A/D ) X V1 =( €A/D - T(1 - 1/K) ) X V2

(€A / 0.3 X 10-2 ) x 6 = ( €A/0.3 X 10-2 - .225 X 10-2(1 - 1/1.7)) x V2

6 / 0.3 = V / 0.3 - 0.092

V = 6 x .208 / .3

V = 4.16volts

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