Question

When 115 V is applied across a wire thatis 11 m long and has a 0.30 mm radius, thecurrent density is 1.3 10⁴ A/m². Find the resistivityof the wire.

1·m

Answer 1

Voltage V = 115 V

Length L =11 m

Radius r= 0.3 mm = 0.3 * 10 ^ -3 m

Current density J = 1.3 * 10 ^ 4 A / m^ 2

Current I = J A

Where A= area = πr ^ 2 = 2.827 * 10 ^ -7 m ^ 2

So, I = 3.675 * 10 ^ -3 A

Resistance R = V / I

                      = 31286.86 ohm

We know R = ρL / A

from this resistivity ρ = RA / L

                              = 8.04 * 10 ^ -4 ohm - m

Answer 2

p=V/(J*L)=115/(1.3e4*11)=8.04e-4

The current density accounts for the resistivity of the area(note that it's units are Amperes/ meters squared). The only element that remains is the voltage difference over the distance (literally and thus mathmatically).