Question

Find the resistance of a 12 meter length of metal wire of 0.5 mm diameter. The resistivity of metal is 2.8×10-6 Ω·cm at a temperature of 20°C. Express the answer with two decimal places.

Answer 1

L = length of wire = 12 m

d = diameter = 0.5 mm = 0.5 x 10^-3 m

A = area of cross-section = $\pi$ d²/4 = (3.14) (0.5 x 10^-3 )² /4 = 1.9625 x 10^-7 m²

$\rho$ = resistivity = 2.8 x 10^-6 ohm-cm = 2.8 x 10^-8 ohm-m

resistance is given as

R = $\rho$ L/A = (2.8 x 10^-8 ) (12) / (1.9625 x 10^-7 ) = 1.71 ohm