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^-3m,

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

We know that C =

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

^{a = 528.6 m2}

a = R²

528.6 = 22/7*R²

^{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