derive an expression to find the resistivity of a conductor?
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The average of velocities v_i of all electrons just after collisions is 0, as they get bounced in all random directions. Hence the average velocity of an electron along the length of a resistor or conductor wire is equal to that gained due to electrostatic field E. So drift velocity = v = e J ρ τ / m --- (2).
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Consider a conductor having length l, area of cross section A and current density n. Therefore, the expression for electrical resistivity is given by ρ=mne2τ.
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