Question

A copper wire has a diameter of 0.5 mm and a resistivity of $1.6\times {10}^{-6}$ ohm-cm. How much of this wire would be necessary to make a resistance of 10 ohm?

Answer 1

Given, $Diameter=0.5mm,resistivity=1.6\times {10}^{-8}\Omega -m,resistance=10\Omega$

we know that $R=\rho \frac{1}{A}\Rightarrow 1=\frac{RA}{\rho }$

Where A is the area of the cross-section,

$=\frac{10\times 3.14\times (\frac{0.0005}{2}{)}^2}{1.6\times {10}^{-8}}=122.7m$

Thus the length of the wire is $122.7m$