Question

Calculate the resistance of copper wire ​having a length of $1\text{km}$ and diameter $0.5\text{mm}$.​
(Resistivity of copper $=1.7\times {10}^{-8}\Omega \text{m}$)

• A. $50\Omega$
• B. $60\Omega$
• C. $75\Omega$
• D. $85\Omega$

Answer 1

The correct option is D $85\Omega$

Given:
Resistivity of copper, $\rho =1.7\times {10}^{-8}\Omega \text{m}$
Length of the wire, $L=1\text{km}=1000\text{m}$
Diameter of wire, $d=0.5\text{mm}=0.5\times {10}^{-3}\text{m}$

Radius of wire, $r=\frac{d}{2}=2.5\times {10}^{-4}\text{m}$
Area of cross section of wire:
$A=\pi r^2$
$A=3.14\times (2.5\times {10}^{-4}{)}^2$
$A\approx 2\times {10}^{-7}{\text{m}}^2$

Resistance is given by:
$R=\frac{\rho L}{A}$
$R=1.7\times {10}^{-8}\times \frac{{10}^3}{2\times {10}^{-7}}$
$R=85\Omega$