Question

What is the resistance of a 100m length of round copper wire with a radius of 0.3mm?
ρ copper=1.724x10−8Ωm

Answer 1

As it is a round wire assume it's area to be area of a circle

Answer 2

Answer:

The resistance of the wire is 6.1Ω.

Explanation:

The value of the  resistance of the wire is given as,

$R=\frac{\rho l}{A}$       (1)

Where,

R=resistance of the wire

ρ=resistivity of the wire

l=length of the wire

A=area of the wire

From the question we have,

l=100m

r=0.3mm=0.3×10⁻³m               (1mm=10⁻³m)

ρ=1.724 ×10⁻⁸Ωm

The area of the cross-section of the wire is given as,

$A=\pi r^2$    (2)

By substituting the value of r in equation (2) we get;

$A=\pi (0.3\times 10^-^3)^2=9\pi \times 10^-^8m^2$   (3)

By substituting the required values in equation (1) we get;

$R=\frac{1.724\times 10^-^8\times 100}{9\pi\times 10^-^8}=0.061\times 100=6.1\Omega$           (∵π=3.14)

Hence, the value of resistance for the wire is 6.1Ω.