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If n, e, tau, m represent electron density, charge, relaxation time, and electron mass respectively, then the resistance of a wire of length l and cross-sectional area A is given by:

1. m*l / (n*e²*tau*A)
2. 2*m*A / (n*e²*tau)
3. n*e²*tau*A
4. n*e²*tau*A / (2*m)

Correct answer: m*l / (n*e²*tau*A)

Solution

In the Drude model of electrical conduction, the drift velocity v_d = eE*tau/m. Current density J = n*e*v_d = n*e²*tau*E/m. By Ohm's law J = sigma*E, so conductivity sigma = n*e²*tau/m. Resistivity rho = 1/sigma = m/(n*e²*tau). Resistance R = rho*l/A = m*l/(n*e²*tau*A). This matches the first option.

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