Question

A wire has a length of 1.20m, a diametee 0.64mm

amd a resistance of 2.4ohms.

calculate the resistance of a wire of the same material of length 0.80 metre and diametre 0.32mm

Answer 1

Given:

$l_1=1.20\:\rm m$

$d_1=0.64\:\rm mm=6.4*10^{-5}\:\rm m$

$l_2=0.80\:\rm m$

$d_1=0.32\:{\rm mm}=3.2*10^{-5}\:{\rm m}=d_1/2$

$R_1=2.4\:\Omega$

The resistance of a wire is given by

$$R=\rho\frac{l}{A}=\rho\frac{l}{\pi d^2/4}$$

Hence

$$R_2=R_1*\frac{l_2}{l_1}*\frac{d_1^2}{d_2^2}\\ =2.4*\frac{0.80}{1.20}*4=6.4\:\Omega$$