An aluminum wire with a diameter of 0.085 mm has a uniform electric field of 0.3

Question

An aluminum wire with a diameter of 0.085 mm has a uniform electric field of 0.315 V/m imposed along its entire length. The temperature of the wire is 35.0 degree C. Assume one free electron per atom. Use the information in this Table of Resistivities and Temperature Coefficients to determine the resistivity of aluminum at this temperature. What is the current density in the wire? What is the total current in the wire? What is the drift speed of the conduction electrons? What potential difference must exist between the ends of a 1.90-m length of the wire to produce the stated electric field?

Explanation / Answer

a) the resistivity is

= 0 [ 1 + ( T - 293 °K ) ]

= 2.82x10-8 .m * [ 1 + 3.9x10-3 °K-1 * ( 308 °K - 293 °K ) ]

= 2.98x10-8 .m

b) the current density of the wire

J = E / = ( 0.315 V/m ) / ( 2.98x10-8 .m ) = 1.06x107 A/m2 = 10.6 MA/m2

c) the total current in the wire is

i = A J = r2 J = ( 4.25x10-5 )2 ( 1.06x107 A/m2 ) = 60.1 mA

d)

I know that

Vd = J / ( e )

where

= at = (Avogadro's number * density ) / (atomic number)

=( 6.02x10^{23} 1/mol * 2700 Kg/m3 ) / ( 26.98x10^{-3} Kg/mol ) = 6.02x10^{28}

Vd = 1099.7 m/s

e) the potential difference is

V = E d = ( 0.315 V/m ) ( 1.90 m ) = 0.599 v

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