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Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area `3.0 xx 10^(-7) m^(2)` carrying a current of 5A. Assume that each copper atom contributions roughly one conduction electron. The density of copper is `9.0 xx 10^(3) kg//m^(3)` and its atomic mass is 63.5 u. |
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Answer» Given corss-sectional area of copper wire, `A = 3 xx 10^(-7) m^(2)` carrying current of copper, I = 5A charge of electron, `e = 1.6 xx 10^(-19) C` Density of conduction electrons = No. of atoms per cubic meter, `n = (N_(A) ("Avogadro number") xx "mass of copper" (M) "per cubic meter")/("Atomic mass"(m))` `:. n = (6 xx 10^(23) xx 9 xx 10^(3))/(63.5) = 8.5 xx 0^(23) m^(-3)` `:.` Average drift speed of conduction electrons. `V_(d) = (I)/(neA) = (5)/(8.5 xx 10^(28) xx 1.6 xx 10^(-19) xxx 3 xx 10^(-7))` `implies V_(d) = (5)/(8.5 xx 1.6 xx 3 xx 10^(2)) = 0.1225 xx 10^(-2) m//s` `:. V_(d) = 1.225 mm//s` |
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