Capacitors with Partial Dielectrics Part A Consider two parallel-plate capacitor

Question

Capacitors with Partial Dielectrics Part A Consider two parallel-plate capacitors identical in shape one aligned so and the other with the plates vertical (Figure 2) The horizontal capacitor is filled halfway with a material that has dielectric constant K What fraction f of the area of the vertical capacitor should be filled (as shown in the figure) with the same dielectric so that the two capacitors have equal capacitance? that the plates are horizontal (Figure 1) Express your answer in terms of K. f= Submit Hints My Answers Give Up Review Part Provide Feedback Continue Figure 1 of 2 d/2

Explanation / Answer

capacitance of capaitor filled with dielectric at t width

C = e0 A / {(d-t)(1 -1/K)}

and t = 0.5d

C = (e0 A) / { 0.5d (K-1)/K }

C = (2K / K-1) (e0 A / d)

for other capacitor:

part filled with dielectric,

C1 = K ( e0 (fA) / d)

other part: C2 = e0 (1-f)A/d

C = C1 + C2 = (e0 A / d) ( fK + 1 - f)

both capacitance are same.

(2K / K-1) (e0 A / d) = ( fK + 1 - f) (e0 A / d)

2K / K-1 = f(K-1) + 1

f(K-1) = (2K - K + 1) / (K-1)

f = (K + 1) / (K-1)^2

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