Copper has a density of 8.92 g/cm3 and a molar mass of 63.5 g/mol. Use these dat

Question

Copper has a density of 8.92 g/cm3 and a molar mass of 63.5 g/mol. Use these data and the fact that there are 6.02 times 1023 atoms / mol to find the number of free electrons per cubic centimeter in copper because there is one free electron per atom on the average. A 14-gauge copper wire (radius 0.0814 cm) carries a current of 1 A. Calculate the drift velocity of the electrons from the equation given in , using n from part (a) and q = e for the charge of each carrier. A galvanometer of resistance 80 Ohm gives a full-scale deflection when its current is 1.2 mA. It is used to construct an ammeter whose full-scale reading is 10 A. Find the shunt resistance needed. If the shunt resistance consists of a

Explanation / Answer

Given Density of copper , = 8.92 g / cm^3 Molar mass , M = 63.5 g / mol Avagadro number , NA= 6.02 *10^23 atoms / mol a) Number of atoms per cm^3 in copper is n = NA * ( / M)    = (6.02 *10^23 atoms / mol) * ( 8.92 g / cm^3) / (63.5 g / mol) n = 8.45 *10^22 / cm^3 or  8.45 *10^28 / m^3 ____________________________________________________ b) Radius of the copper wire , r = 0.0814 cm Current in the wire , i = 1 A Nunber of atoms per cm^3 is  8.45 *10^22 / cm^3 Area of cross section, A = r^2 = 3.14 * (0.0814 *10^-2 m)^2 = 2.08 *10^-6 m^2 Drift velocity , vd = i / n e A                              = 1 A / ( 8.45 *10^28 / m^3) (1.6 *10^-19 C) * 2.08 *10^-6 m^2                          vd = 2.8 *10^4 m/s

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