Question

There are two identical capacitors the first one is uncharged

Answer 1

The complete question is,

There are two identical capacitor,the first one is uncharged and filled with dielectric constant K. while other is charged to potential V having air b/w its plate.if they are joined end to end,the common potential will be?

Given:

There are two identical capacitors,the first one is uncharged and filled with dielectric constant K. while other is charged to potential V having air b/w its plate.

To find:

If they are joined end to end, the common potential will be?

Solution:

From given, we have,

There are two identical capacitors, the first one is uncharged and filled with dielectric constant K. while other is charged to potential V having air b/w its plate.

As the charge will flow from  C₂  to  C₁ until their potential become equal, let us consider common potential be V1.

The  capacitor C₁ is given by, θ₁ = KC₀V₁

Similarly, the capacitor C₂ is given by, θ₂ = C₀V₁

using conservation law, we have,

θ₁ + θ₂ = θ

K C₀V₁ +  C₀V₁  = C₀V

where C₀V is the charge on the capacitor C₂

Thus, we get

(K + 1) C₀V₁  = C₀V

V₁ = V/(K + 1)

Thus if they are joined end to end, the common potential will be V₁ = V/(K + 1)