What is the resistance of a wire made of a material with a resistivity of 3.2 *10-8 $\Omega$ . m if its length is 2.5 m and its diameter is 0.50 mm?
A)0.16 $\Omega$
B)0.10 $\Omega$
C)1.28 $\Omega$
D)0.41 $\Omega$
E)0.81 $\Omega$

Question

Quizplus · Accepted Answer

We can use the formula for resistance of a wire:

R = ρL/A

where: 
ρ = resistivity of the material (3.2 x 10^-8 Ω·m) 
L = length of the wire (2.5 m) 
A = cross-sectional area of the wire (πr^2, where r is the radius or half of the diameter)

First, we need to convert the diameter to radius and then to meters:

0.50 mm = 0.50 x 10^-3 m

Radius = diameter/2 = 0.25 x 10^-3 m

Area = π(0.25 x 10^-3 m)^2 = 1.96 x 10^-7 m^2

Now we can substitute into the formula:

R = (3.2 x 10^-8 Ω·m)(2.5 m)/(1.96 x 10^-7 m^2)

R = 0.41 Ω

Therefore, the correct answer is D) 0.41 Ω.

What Is the Resistance of a Wire Made of a Material