# Cylindrical Capacitor Formula

The capacitor is used to store large amounts of electric current in a small space. Capacitors include wide applications in electric juicers, electric motors, flour mills and other electrical instruments. The potential difference between each capacitor varies. There are many electrical circuits where capacitors are to be grouped accordingly to get the desired capacitance. There are two common modes including capacitors in series and capacitors in parallel. The unit of capacitance is Farad(F).

It is often used to store the electric charge. The Cylindrical capacitor is a type of capacitor that possess the shape of a cylinder having an inner radius as a and outer radius as b.

The formula for the cylindrical capacitor is

$C=2\pi \epsilon _{0}L/\l n(\frac{b}{a})$

Where,

C= capacitance of the cylinder

L = length of the cylinder

a =  inner radius of the cylinder,

b = outer radius of the cylinder

$\epsilon _{0}$ = permittivity of free space ($8.85X10^{-12}$)

Problem 1: A Cylindrical capacitor having a length of 8 cm is made of two concentric rings with an inner radius as 3 cm and outer radius as 6 cm. Find the capacitance of the capacitor.

Given:

Length L = 8 cm

inner radius a = 3 cm

outer radius b = 6 cm

Formula for cylindrical capacitor is

$C=2\pi \epsilon _{0}L/\l n(\frac{b}{a})$

$C=(2)(3.14)(8.85*10^{-12})(8*10^{-2})/\l n(\frac{6}{3})$
$C=444.62X10^{-14}/0.301$
$C=1.477 X 10^{-11}F$.