A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm.
a) Calculate the capacitance.

b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.

Question

Philoid · Accepted Answer

Given

Length, l = 10cm

Radius, R₁ = 2mm

Radius, R₂ = 4mm

Formula used :

a) The capacitance of the cylindrical capacitor is given by

Where

l→ length of the cylinder

R₂→ radius of outer cylinder

R₁→ radius of inner cylinder permittivity of the free space

ε₀→ permittivity of the free space = ε₀=

Putting the value in the above formula, we get

b) Another cylindrical capacitor of same but different radius R₁=4mm and R₂= 8mm

If we compare the radii in a) with b), they give the same ratio

So capacitance is also same as a) is

Capacitance of cylindrical capacitor for both a) and b) is same and is =8pF

A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm.a) Calculate the capacitance.b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.