Question

An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air cored parallel capacitor charged to potential V. the two capacitors share charges and the common potential is V the dielectric constant K is ​

Answer 1

The value of constant K is K = V - V'/V'

Explanation:

Using the formula:

V' = C1V1 + C2V2/ C1 + C2

Charge of I capacitor is Q = 0

=> C1V1 = 0

V' is the common potential i.e. V'=V'

V2 = V

C1 = Kε0A/d  and C2 = ε0A/d

And

V' = 0+ε0A/d (V) /  Kε0A/d + ε0A/d

V' = ε0A/d (V) / ε0A/d[K + 1]

K + 1  = V/V'

K = V/V' - 1

K = V - V'/V'

Thus the value of constant K is K = V - V'/V'

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