A parallel plate capacitor has plates of area A and plate separation d. It is fi

Question

A parallel plate capacitor has plates of area A and plate separation d. It is filled with three slabs of dielectric, side by side. Each slab takes up area A/3, and the slabs have dielectric constants K, 2K, and 1.7K. Find the total capacitance as a multiple of (Epsilon naught)A/d (and explain your answer).

A parallel plate capacitor has plates of area A and plate separation d. It is filled with two equally-sized slabs of dielectric, joined together in the middle. The slabs have dielectric constants K and 1.7K. Find the total capacitance as a multiple of (Epsilon naught)A/d (and explain your answer)

Explanation / Answer

a)

for three dielectric slabs, these all three capacitance will be in parallel

capacitance C = K*e0*A/d

now for this combination

C = C1 + C2 + C3 = K*e0*(A/3)/d + 2K*e0*(A/3)/d + 1.7K*e0*(A/3)/d = 1.567*K*e0*A/d

b)

now for this, this combination like series so

C1 = K*e0*A/(d/2)

C2 = 1.7K*e0*A/(d/2)

C = C1*C2/(C1+C2) = (K*e0*A/d)*(2*3.4/(2+3.4)) = 1.26*K*e0*A/d

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