Question

A coaxial cable of radii 5 mm and 3 mm is connected by a battery of 12 V. If the charge on each cable is 6 nC, the length of the capacitor is ?

Answer 1

Since,

Capacitance = C = Q/V

here, Q = 6 nC = 6*10^-9 C

V = 12 V

So, C = (6*10^-9)/12

C = 5*10^-10 F

now , capacitance of a cylindrical capacitor = C = (2*pi*o*L)/ln(Ro/Ri)

here, Ro = outer radius = 5 mm = 5*10^-3 m

Ri = inner radius = 3 mm = 3*10^-3 m

L = length of capacitor = ??

So, C = (2*pi*(8.85*10^-12)*L)/ln(5/3)

L = [(5*10^-10)*ln(5/3)]/(2*pi*(8.85*10^-12))

L = 4.59 m

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