Cylindrical capacitor Formula

The capacitance for a cylindrical geometry, is the capacitance stated as a capacitance per unit length. The charge resides on the outer surface of the inner conductor and the inner wall of the outer conductor. It depends on the inner and outer radius.

Capacitance per unit length = 2 * π * (relative permittivity) * (permittivity of space) /Logarithm (outer radius / inner radius )

The equation is:

C =2 π k ϵ /Log(ro/ri)

Where:

C: Capacitance

ri: inner radius

ro: outer radius

k: relative permittivity

ϵ: permittivity of space

Cylindrical capacitor Formula Questions:

1) A cylindrical capacitor filled with air is formed by to cylinders with inner radius 1 cm, and outer radius 5 cm. What is its capacitance?

Answer:

From the cylinder capacitance formula, we substitute the permittivity, equals to one for air, and both radius:

C =2 π k ϵ /Log(ro/ri) = 2 π (8.854 *10^(-12) F/m) /Log( 5 cm/ 1 cm)

C = 55.63*10^(-12) F/m /Log(5)= 79.6*10^(-12) F/m

2) A cylindrical capacitor filled with paper is formed by to cylinders with inner radius 2 cm, and outer radius 5 cm. What is its capacitance?

Answer:

From the cylinder capacitance formula, we substitute the permittivity, equals to 3.85 for paper, and both radius:

C =2 π k ϵ /Log(ro/ri) = 2 π (8.854 *10^(-12) F/m)*(3.85) /Log( 5 cm/ 2 cm)

C = 3.85*55.63*10^(-12) F/m /Log(2.5)= 538.22*10^(-12) F/m