Question

An iron wire with a diameter of 0.80mm will have a resistance of 0.4ohms. What resistance will the iron wire of 0.40mm diameter have if it has the same length as the iron wire?

Answer 1

We know that

$R=\frac{\rho l}{A}$

$\frac{R_1}{R_2}=\frac{l_1A_2}{l_2A_1}$

$A=\pi r^2$

$\frac{R_1}{R_2}=\frac{l_1r^2_2}{l_2r^2_1}$

$R_2=R_1\times\frac{l_2r^2_1}{l_1r^2_2}$

$l_1=l_2$

$R_2=0.4\times\frac{(0.80\times10^{-3})^2}{(0.40\times10^{-3})^2}$

$R_2=1.6\Omega$