Question

upper plate (area A) K2 d Imagine a parallel plate capacitor made from two square plates of area A that are separated by a distance 2d. One half of the volume between the plates is filled with a dielectric material with a dielectric constant K1; the other half is filled with two equal, stacked layers of dielectric materials with constants K2 and K3, as shown. Find the capacitance of this capacitor. 2d K1 K3 d bottom plate (area A)

Answer 1

It acts as a combination of three capacitors.

C1 = k1*(A/2)*epsilon/(2*d)

= k1*A*epsilon/(4*d)

C2 = k2*(A/2)*epsilon/d

= k2*A*epsilon/d

C3 = k3*(A/2)*epsilon/d

= k3*A*epsilon/d

here C2 and C3 are in series.

so, C23 = C2*C3/(C2 + C3)

= (k2*k3/(k2 + k3))*(A/2)*epsilon/d

C23 is in parallel with C1

so, effective capacitance, C = C1 + C23

= k1*A*epsilon/(4*d) + (k2*k3/(k2 + k3))*(A/2)*epsilon/d

= (A*epsilon/d)*(k1/4 + (1/2)*k2*k3/(k2 + k3) ) <<<<<<<<----------Answer