Question

A 6.60-m length of 2.1-mm-diameter wire carries a 790 mA current when 24.0 mV is applied to its ends.

a) Determine the resistance RR of the wire.

b) Determine the resistivity ρρ.

c) If the drift speed is 1.9×10⁻⁵m/s, determine the number n of free electrons per unit volume.

Answer 1

(a) Resistance = voltage / Current = ( 24 10^-3 ) / ( 790 10^-3 ) = 3.038 10^-2

(b) Resistivity is calculated using the following formula

Resistance R = ( L / A ) , where L is length of wire and A is area of crossection of wire

= R ( A / L) = 3.038 10^-2 ( 1.05 1.05 10^-6 ) / 6.6 = 1.594 10^-8-m

(c) Number density n of free electron is calculated from the following formula

I = n e v A

where I is current , e is charge on electron, v is drift speed and A is area of conducting wire

n = I / ( e v A ) = (790 10^-3 ) / [ 1.602 10^-19 1.9 10^-5 ( 1.05 1.05 10^-6 ) ]

free electron density n = 7.493 10²⁸ m^-3