An aluminum wire with a diameter of 0095 mm has a uniform el

An aluminum wire with a diameter of 0.095 mm has a uniform electric field of 0.305 V/m imposed along its entire length. The temperature of the wire is 35.0° C. Assume one free electron per atom. (a) Use the information in the Table of Resistivities and Temperature Coefficients to determine the resistivity of aluminum at this temperature. ? = ?m (b) What is the current density in the wire? J = MA/m2 (c) What is the total current in the wire? I = mA (d) What is the drift speed of the conduction electrons? vd = ?m/s (e) What potential difference must exist between the ends of a 1.90-m length of the wire to produce the stated electric field?

Solution

p = p₀ [1 + alpha (T - T₀)]

= 2.82 * 10^-8 [1 + (3.9 * 10^-3) (35 - 20)]

= 2.98 * 10^-8 ohm.m = 29.8 nohm.m

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J = [1 / p] * E = [1 / (2.98 * 10^-8)] * 0.305

= 10.23 * 10⁶ A/m²

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I = 10.23 * 10⁶ * pi * (0.0475 * 10^-3)²

= 7.25 * 10^-2 A = 72.5 mA

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e) From the relation between electric field vector an potential

= 0.305 V/m * 1.90 m

= 0.58 V