A wire of unknown material has a cross-sectional area 7 mm 2 and length 15 cm. T

Question

A wire of unknown material has a cross-sectional area 7 mm2 and length 15 cm. The wire carries current density J = 4 ?C/s/m2 and has a voltage difference of 25 V held constant across its ends.

What is total current in the wire?

What is the resistivity of the unknown material?

At what rate is electromechanical energy being converted into thermal energy in this wire?

If the unknown material has a free electron density of 8 x 1028 electrons/m3, how long does it take for an electron to travel the length of the wire?

Explanation / Answer

I = J A = 4.0E-6*7.0E-6=2.8E-11 A

R = rho L/A and V = I R

25 = 2.8E-11*rho*.15/7.0E-6

rho=4.17E7

P = V^2/R = 25^2/(2.8E-11*4.17E7*.15/7.0E-6)=24.98 W

v = I/ n A q but v = L/t

.15/t = 4.0E-6/(8.0E28*1.6E-19)

t=4.8E14 s

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