Answer to Question #171846 in Electricity and Magnetism for loysie

Question

the resistance of a rod with a length of 3.0m and a diameter of 1.0cm is 56.0 ohms. of this rod is stretched to form a wire with a diameter of 0.01cm, what is its resistance? assume that in the process of stretching the rod, its volume did not change.

Answer 1

$R=\frac{\rho l}{S}=\frac{4\rho l}{\pi d^2},$

$V=\pi d^2l,\implies l=\frac{V}{\pi d^2},$

$R=\frac{4\rho V}{\pi^2 d^4},$

$R\sim \frac{1}{d^4},$

$R_2=R_1\cdot \frac{d_1^4}{d_2^4},$

$R_2= 56\cdot \frac{1^4}{0.01^4}=5.6~G\Omega.$