Question

Find the capacitance of the following parallel plate capacitor, filled with differing amounts of dielectric materials. The empty space is air and here k = 1.

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Answer 1

here ,

for the net capacitance Ceq

C1 = epsilon_0 * 3 * (3/4 * L^2)/(d/2)

C1 = epsilon_0 * 9*L^2/(2d)

C2 = epsilon_0 * (3L/4 * L)/(d/2)

C2 = epsilon_0 * (3/2 * L^2)/d

C3 = epsilon_0 * (5*L^2/2)/d

Now , for the net capacitance

1/C4 = 1/C2 + 1/C1

1/C4 = 1/(epsilon_0 * (3/2 * L^2)/d) + 1/(epsilon_0 * 9*L^2/(2d))

C4 = 1.125 * epsilon_0 * L^2/d

Ceq = C3 + C4

Ceq = (1.125 + 2.5) * epsilon_0 * L^2/d

Ceq = (3.625 * 8.854 *10^-12 * 0.08^2)/.010

Ceq = 2.054 *10^-11 F

the net capacitance is 2.054 *10^-11 F