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Potential difference of 100 V is applied to the ends of a copper wire one metre long. Calculate the average drift velocity at 27^@ C . Assume that there is one conduction electron per atom. The density of copper is 9.0xx10^3 kg//m^3 , Atomic mass of copper id 63.5 g. Avogadro's number =6.0xx10^(23) per gram- mole. Conductivity of copper is 5.81xx10^(7) Omega^(-1) . Boltzmann constant =1.38xx10^(-23) JK^(-1). |
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Answer» Solution :Here , `V= 100 V , l = 1 m` M= 63.5 g = `63.5 xx 10^(-3) Kg` `rho = 9.0xx10^3 kg//m^3` `N = 6.0xx10^(23) ` per GRAM- mole, `sigma = 5.81 xx 10^7 Omega^(-1)` SINCE `6 xx 10^(23)` copper atoms have a MASS of 63.5 g , and there is one conduction electron per atom, number of electrons per unit volume is `n = (6.0xx10^(23))/(63.5xx10^(-3)) xx9.0xx10^3 kg//m^3 = 8.5xx10^(28) m^(-3)` ELECTRIC field `E= V/l = (100)/(1) = 100 Vm^(-1)` As J = `sigmaE= "ne"v_d` `therefore V_d = (sigmaE)/("ne") = ((5.81xx10^7) xx(100))/((8.5xx10^(28)) xx 1.6xx10^(-19)) = 0.43 MS^(-1)` Thermal velocity `v_("rms") = sqrt((3k_B T)/(m_e))` `= sqrt((3xx 1.38xx 10^(-23) xx 300)/(9.1xx10^(-31))) = 1.17xx10^5 ` m/s `(V_d)/(V_(rms)) = (0.43)/(1.17xx10^5) = 3.67xx10^(-6)` |
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