Consider a parallel-plate capacitor constructed from two circular metal plates o

Question

Consider a parallel-plate capacitor constructed from two circular metal plates of radius R. The plates are separated by a distance of 1.5 mm. (a) What radius must the plates have if the capacitance of this capacitor is to be 3.0 mu F? m (b) If the separation between the plates is decreased, should the radius of the plates be increased or decreased to maintain a capacitance of 3.0 mu F? decreased increased Explain. (c) Find the radius of the plates that gives a capacitance of 3.0 mu F for a plate separation of 3.0 mm.

Explanation / Answer

(a)
d = 1.5 x 10^-3 m
C = 3 x 10^-6 F
C = eo * A/d
A = C * d/eo
A = 3 x 10^-6 * 1.5 x 10^-3/(8.8542 * 10^-12)
A = 508.233 m^2
A = pi * R^2
R = sqrt(A/pi) = sqrt(508.233 /pi) = 12.71 m
Ans: 12.71 m

(b)
increased
From the formula C = eo * A/d,
if d is increased, then A should be increased to maintain
the same capacitance. From the formula A = pi * R^2,
if A increases, then R increases.

(c)
d = 3 x 10^-3 m
C = 3 x 10^-6 F
C = eo * A/d
A = C * d/eo
A = 3 x 10^-6 * 3 x 10^-3/(8.8542 * 10^-12)
A = 1016.466 m^2
A = pi * R^2
R = sqrt(A/pi) = sqrt(1016.66 /pi) = 17.98 m
Ans: 17.98 m

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