Question

Consider a parallel-plate capacitor constructed from two circular metal plates of radius R. The plates are separated by a distance of 1.8 mm. (a) What radius must the plates have if the capacitance of this capacitor is to be 2.6 µF? 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 2.6 µF? increased decreased Explain. This answer has not been graded yet. (c) Find the radius of the plates that gives a capacitance of 2.6 µF for a plate separation of 3.0 mm. m

Answer #1

Given distance between plates d = 1.8mm =
1.8*10^{-3}m,

a) capacitance C = 2.6*10^{-6}F.

We know that C =

I.e. 2.6*10^{-6} =
8.854^{-12}*a/1.8*10^{-3}

^{a = 528.6 m}^{2}

a = R^{2}

528.6 = 22/7*R^{2}

^{R = 13 m}

^{b) if the distance between the plates decreased and kept
the capacitance constant the area must be decreased}

^{because C is proportional to area of the plates and
inversely proportional to distance between the
plates}

^{c) C = a/d}

2.6*10^{-6} =
8.854*10^{-12}*a/3*10^{-3}

a = 881 m^2

R = 16.75m

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