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Derive an expression for the resistivity of a good conductor in terms of the relaxation time of electrons. |
Answer» SOLUTION :  On applying a potential difference V across the ends ofa conductor of length l, the electric field `E = V/l` Force experienced by an electron`F = eE = (eV)/(l)` in a direction opposite to that of E. `therefore `ACCELERATION of electron in a direction opposite to that of E will be `a = F/m = e/m.V/l` If the average time between two successive collisions suffered by an electron be `TAU` , the drift velocity of electron will be `v_d = a tau = e/m . V/l. tau`....(i) But in terms of drift velocity magnitude of electric current is given by `I = nAev_d = nAe. e/m.V/l.tau = (nAe^2)/(m) tau. V/l` ` therefore ` RESISTANCE of conductor`R = V/l = (ml)/(nAe^2 tau)`.....(ii) and resistivity of the material of conductor `rho = (RA)/(l) = (m)/("ne"^2 tau)`....(iii) The resistivity of a material thus depends on (i) the number density of electrons, and (ii) its relaxationtime. |
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