Question

Q1: Calculate the diameter of a copper conductor 300 m long such that it may carry 500 A with a voltage drop of 8 V. The resistivity of the copper may be taken as 0.019  m.

Answer 1

The diameter of a copper conductor is equal to 21.30 meters.

Given the following data:

• Length = 300 m

• Current = 500 A

• Voltage = 8 V

• Resistivity = 0.019

To calculate the diameter of a copper conductor:

First of all, we would determine the resistance of the copper conductor by using the formula:

$Resistance = \frac{Voltage }{Current} \\\\Resistance =\frac{8}{500}$

Resistance = 0.016 Ohms

Next, we would determine the area of the copper conductor:

$Resistance = \frac{\rho l}{Area} \\\\Area = \frac{\rho l}{Resistance}\\\\Area = \frac{0.019 \times 300}{0.016}$

Area = 356.25 $m^2$

For the diameter:

From the area of a circle, diameter is given by the formula:

$Area = \frac{\pi d^2}{4} \\\\d=\sqrt{\frac{4A}{\pi} } \\\\d=\sqrt{\frac{4 \times 356.25}{3.142} }\\\\d=\sqrt{453.53}$

Diameter, d = 21.30 meters

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