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,

$\begin{gathered} P=I^2R \\ =\frac{I^2\rho l}{A} \\ =\frac{I^2\rho l}{\pi r^2} \end{gathered}$

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,

$p=\frac{P}{l}=\frac{I^2\rho}{\pi r^2}$

On rearranging the above equation,

$r=\sqrt[]{\frac{I^2\rho}{\pi p}}$

On substituting the known values,

$\begin{gathered} r=\sqrt[]{\frac{300^2\times1.7\times10^{-8}}{\pi\times2}} \\ =0.016\text{ m} \\ =1.6\text{ cm} \end{gathered}$

Thus the radius of the cable is 1.6 cm