Question

Two parallel plate capacitors x and y have the same area of plates and same separation between them. X has air between the plates while y contains a dielectric medium of r = 4 (i) calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 f. (ii) calculate the potential difference between the plates of x and y. (iii) estimate the ratio of electrostatic energy stored in x and y.

Answer 1

We know that capacitance for a parallel plate capacitor

C= ε₀KA/d

For air, K=1, so capacitance for x, C(x)=ε₀ A/d

Capacitance for y, C(y)=ε₀4K/d= 4C(x)

We know, 1/C= 1/C(x) + 1/C(y)

       A/Q, 1/4= 1/C(x) + 1/C(y)

               1/4= 1/C(x) + 1/ 4C(x)

               1/4= 1/C(x) {1+  1/4}

                   = 1/C(x) {5/4}

         1/C(x)= 1/5

           C(x)= 5 f

So, 1/C(y)= (1/4)- (1/5)

               = 1/20

 C(y)= 20 f

(ii) We know, Q= CV, where V is the potential difference of the plane.

           For, x,

  Potential difference V(x) = Q/C(x)

   V(x) = Q/5f

For y  

Potential difference V(y) = Q/Cy

V(y) = Q/20f

(iii) Now, energy stored in capacitor E= Q²/2C

       For E(x)= Q²/2C(x)= Q²/10

  For, E(y)= Q²/2C(y) = Q²/40

Ratio of energy, E(x)/E(y)= {(Q²/10)/(Q²/40)}

                                        = 4/1

       

Answer 2

Answer:

We know that capacitance for a parallel plate capacitor

C= ε₀KA/d

For air, K=1, so capacitance for x, C(x)=ε₀ A/d

Capacitance for y, C(y)=ε₀4K/d= 4C(x)

We know, 1/C= 1/C(x) + 1/C(y)

       A/Q, 1/4= 1/C(x) + 1/C(y)

               1/4= 1/C(x) + 1/ 4C(x)

               1/4= 1/C(x) {1+  1/4}

                   = 1/C(x) {5/4}

         1/C(x)= 1/5

           C(x)= 5 f

So, 1/C(y)= (1/4)- (1/5)

               = 1/20

 C(y)= 20 f

(ii) We know, Q= CV, where V is the potential difference of the plane.

           For, x,

  Potential difference V(x) = Q/C(x)

   V(x) = Q/5f

For y  

Potential difference V(y) = Q/Cy

V(y) = Q/20f

(iii) Now, energy stored in capacitor E= Q²/2C

       For E(x)= Q²/2C(x)= Q²/10

  For, E(y)= Q²/2C(y) = Q²/40

Ratio of energy, E(x)/E(y)= {(Q²/10)/(Q²/40)}

                                        = 4/1

thank you mate . hope it helps you