Two different capacitors have the same plate separation. However, one capacitor

Question

Two different capacitors have the same plate separation. However, one capacitor is made with square plates, while the other if made of circular plates. The square plates have a length L on each side, and the diameter of the circular plates is L.
a) If the same dielectric material were between the plates in each capacitor, which one would have the greater capacitance? Explain.
b) By putting different dielectric materials between the capacitor plates, the two capacitors can be made to have the same capacitance. Which capacitor should contain the dielectric material with the greater dielectric constant? Explain.
c) The capacitors have the same capacitance because they contain different dielectric materials. The dielectric constant of the material between the square plates has a value ofk square = 3.00. What is the dielectric constant kcircle of the material between the circular plates? Be sure your answer is consistent with your answers to the concept questions above.

Explanation / Answer

Here ,

as the capacitance is given as

C = Area * epsilon_0/seperation

a) area of square plate = L^2

area of circle plate = pi * (L/2)^2

area of circle plate = 0.785 * L^2

as the area of square plates is higher , the capacitor with Square plate will have higher capacitance

b) For same capacitance ,

C = dielectric constant * Area * epsilon_0/seperation

hence , to balance the effect of area ,

the circular plate capacitor must have greater dielectric constant

c)

let the dielectric constant of circular capacitor is kc

then

area * dielectric constant is same for both capacitors

L^2 * 3 = 0.785 * L^2 * kc

kc = 3.82

the dielectrinc constant of material between circular plates is 3.82

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