Question

A copper cable carries a current of 300 A. If the power loss is 2 W per meter, find the radius of the cable. (The resistivity of copper is 1.7x10-8 Ωm.) Group of answer choices1.6 cm0.80 cm4.0 cm3.2 cm

Answer 1

Given,

The current carried by the cable, I=300 A

The power loss per meter, p=2 W

The resistivity of the copper, ρ=1.7×10⁻⁸ Ωm

The power loss of a conductor is given by,

`\begin{gathered} P=I^2R \\ =(I^2\rho l)/(A) \\ =(I^2\rho l)/(\pi r^2) \end{gathered}`

Where;

• R is the resistance of the wire.

,

• l is the total length of the wire.

,

• A is the cross-sectional area of the cable.

,

• r is the radius of the cable.

The power loss per meter is given by,

`p=(P)/(l)=(I^2\rho)/(\pi r^2)`

On rearranging the above equation,

`r=\sqrt[]{(I^2\rho)/(\pi p)}`

On substituting the known values,

`\begin{gathered} r=\sqrt[]{(300^2*1.7*10^(-8))/(\pi*2)} \\ =0.016\text{ m} \\ =1.6\text{ cm} \end{gathered}`

Thus the radius of the cable is 1.6 cm