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A conductor of length l is connected to a.d.c, source of potential V. If the length of the conductoris tripled by stretchingit, keeping V constant, explain how do the following factors vary in the conductor ? (i) Drift speed of electrons (ii) Resistance (iii) Resistivity. |
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Answer» Solution :When the WIRE is stretched to thrice its LENGTH the area is reduced to thrice its length, the area is reduced to ONE - thrid. `:.` Let `l_1 = l, l_2 = 3l, A_1 = A, A_2 = A//3` Now `R_1 = rho(l_1)/A_1 and R_2 = rho (l_2)/A_2` `R_2/R_1 = (l_2/l_1) xx(A_1/A_2) = 3 xx 3 = 9` or `R_2 = 9R_1` i.e. resistance will become 9 times. Resistivity depends upon the nature of the material of the conductor and TEMPERATURE. It does not depend upon the dimensions of the wire. Since meterial of the wire and the temperature remain constant,HENCE resistivity will remain constant. Drift vel., `v_d = (eEtau)/m = (eV tau)/(ml)` Since, e, V, `tau` and m are constant, hence when lenght is tripled, the drift velocity becomes `1/3rd` that of the original length. |
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