Question

A capacitor is half filled with a dielectric(K= 2) as shown in figure A. If thesame capacitor is to be filled with samedielectric as shown, what would be thethickness of dielectric so that capacitorstill has same capacity?​

Answer 1

Answer:

2d/3 is the thickness of dielectric so that capacitor still has same capacity

Explanation:

solution :

Capacitance  of capacitor for Fig 1 is :

C1= Ak ε₀/2d + Aε₀/2d

= (k+1) Akε₀/2d

According to question k=2

so

C1=3Akε₀/2d ---------------(1)

For figure 2:

C2= Aε₀/ [(d-t) + t/2]

=2Aε₀/[2d-2t+t]

=2Aε₀/2d-t ----------2

According to question C1= C2

3Aε₀/2d=2Aε₀/2d-t

6d-3t=4d

2d=3t

t=2d/3