Question

Resistance of a metal wire of length 15km is 450 Kilo ohm at 20°c. If the diameter of the wire is 0.25mm, what will be the resistivity of the metal at that temperature?

Answer 1

Given that,

Resistance =450 kΩ

Length = 15 km

Diameter = 0.25 mm

Temperature = 20°C

We need to calculate the resistivity of the metal at that temperature

Using formula of resistivity

$\rho=\dfrac{RA}{l}$

Where, R = resistance

l = length of wire

A = area of wire

Put the value into the formula

$\rho=\dfrac{450\times10^{3}\times\pi\times(\dfrac{0.25\times10^{-3}}{2})^2}{15\times10^{3}}$

$\rho=0.000001473\ \Omega-m$

$\rho=1.473\times10^{-6}\ \Omega-m$

Hence, The resistivity of the metal at that temperature is $1.473\times10^{-6}\ \Omega-m$