Question

Determine the resistance of a copper wire having a length of $1km$ and diameter of $0.5mm$. Resisivity of copper $=1.7\times {10}^{-3}\Omega m$.

• A. 85
• B. 90
• C. 40
• D. 30

Answer 1

The correct option is (A) $85\Omega$
$\rho =$ Resisivity of copper $=1.7\times {10}^{-3}\Omega m$
convertung all measures into metres.
$L=1km=1000m={10}^{3}m$
$d=0.5mm=0.5\times {10}^{-3}m$
If $r$ is the radius of the wire then, its area of cross-section
$A=\pi r^2$
$\therefore A=\pi \times {\left(\frac{d}{2}\right)}^2$
$=\frac{\pi }{4}(0.5\times {10}^{-3}{)}^2{m}^2$
$R=\rho \frac{L}{A}=\frac{1.7\times {10}^{-3}\Omega m\times \left({10}^{3}m\right)}{0.2\times {10}^{-3}{m}^2}=85\Omega$