Question

Show all work and explain how you get the correct answer of C.

A parallel plate capacitor with plates of area A and separation d is initially filled with air. Then a dielectric with dielectric constant K, thickness d and area A/2 is inserted into the capacitor such that it fills half the volume of the capacitor. What is the capacitance of this half-dielectric-filled. half-air-filled capacitor? A. K elementof_0 A/2d B. Kelementof_0 A/d C. elementof_0A/2d (K + 1) D. elementof_0A/2d (K/K +1)

Answer 1

10. we know that capacitance is given by:

C = k*e0*A/d

Since it's half dielectric filled and half air field, which means capacitors are in parallel connection

In parallel circuit

Ceq = C1 + C2

C1 = capacitance of dielctric filled capacitor = K*eo*(A/2)/d = K*e0*A/2d

C1 = capacitance of Air filled capacitor = 1*eo*(A/2)/d = e0*A/2d

So,

Ceq = K*e0*A/2d + e0*A/2d

Ceq = (e0*A/2d)*(K+1)