Problem #4 (Due 1/29 Friday by 9:00 a.m.) Two different capacitors have the same

Question

Problem #4 (Due 1/29 Friday by 9:00 a.m.)
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 of k 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

A) Capacitance = 0A/d

area of square = L^2

area of circle = pi*L^2/4

Since area of circle is less than square, so square capacitor will have greater capacitance

B) Circle because its area is less so higher dielectric constant is needed to make capacitance same.

C) K_square*0A_square/d = K_circle*0A_circle/d

=> K_square*A_square = K_circle*A_circle

=> K_circle = K_square*A_square/A_circle = 3*L^2/(pi*L^2/4) = 3*4/pi = 3.819 Answer

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