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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 ?
ρcu = 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
ρAl = 2.8 x 10-8 ? -meter
= 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
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