Question

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

Answer 1

The capacitance is `=8 pF`

Explanation:

The capacitance of a cylindrical cylinder is

`C=(2piepsilon_0epsilon_rL)/(ln(b/a))`

Calculation for the first cylinder.

The length of the cylinders is `L=0.1m`

The radius of the small cylinder is `a=0.002m`

The radius of the large cylinder is `b=0.004m`

The dielectric constant for air is `epsilon_r=1.0006`

The permittivity of vacuum is `epsilon_0=8.85*10^-12 Fm^-1`

Therefore,

The capacitance of the first capacitor is

`C_1=(2pi*1.0006*8.8510^-12*0.1)/(ln(0.004/0.002))`

`=8*10^-12F`

`=8pF`

Calculation for the second cylinder.

The length of the cylinders is `L=0.1m`

The radius of the small cylinder is `a=0.004m`

The radius of the large cylinder is `b=0.008m`

The dielectric constant for air is `epsilon_r=1.0006`

The permittivity of vacuum is `epsilon_0=8.85*10^-12 Fm^-1`

Therefore,

The capacitance of the first capacitor is

`C_1=(2pi*1.0006*8.8510^-12*0.1)/(ln(0.008/0.004))`

`=8*10^-12F`

`=8pF`