Calculate the diameter of copper wire of length 100 metres used as winding material in a transformer such that the resistance of the whole winding is 2 ohms. Calculate the diameter of wire if aluminium is to be used for the above winding, resistance remaining the same. Given the resistivity of Cu are 1.72 × 10^-8 ohm-metres and of AI are 2.8 × 10^-8ohm-metres.

Ans:

L = 100 meter

R = 2 ?

ρ_cu = 1.72 x 10^-8 ? -meter

R = ρ (l/A)

= 1.72 x 10^-8 x 100/A = 2

A = 1.72 x 10^-8 x 100/2

= 0.86 x10^-6

πr² = 0.86 x10^-6

r² = 0.86 x10^-6 / π

= 0.274 x 10^-6

r = 0.523 x 10^-3

Diameter = 1.047 x 10^-3 meter

For Aluminium

ρ_Al = 2.8 x 10^-8 ? -meter

R = ρ (l/A)

= 2.8 x 10^-8 x 100/A = 2

A = 2.8 x 10^-8 x 100/2

= 1.4 x10^-6

πr² = 1.4 x10^-6

r² = 1.4x10^-6 / π

= 0.446 x 10^-6

r = 0.667 x 10^-3

Diameter = 1.335 x 10^-3 meter