A metal has a resistivity rho = 6.00 Times 10^-8 Ohm meters at 30.0 degree C. It

Question

A metal has a resistivity rho = 6.00 Times 10^-8 Ohm meters at 30.0 degree C. It is made into cables of circular cross-section of radius 0.250 mm. What length of conductor will have a resistance of 100 Ohms at this temperature? Calculate the average drift velocity of the electrons in this length conductor at this temperature when a 20 Volt potential difference is maintained between its ends. (The number of conduction electrons per unit volume for this metal is known to be n = 256 Times 10^29m^-3, and the charge on an electron is -e = -1.60 Times 10^-19 C)

Explanation / Answer

R = L / A

100 = 6.00 * 10^-8 * L / pi*(0.25 * 10^-3)^2

So, L = 327.249 m

The average velocity with which electrons must pass along a conductor to carry a current, I, is

u(drift) = I / enA

I = V/R = 20/100 = 0.2 A

So, u = 0.2 / (-1.6*10^-19 * 2.56 * 10^29 * pi*(0.25 * 10^-3)^2) = -0.0000248680 = -2.486 * 10^-5

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