Explanation Given info: The cross-sectional area of aluminum wire is 4.00 × 10 − 6 m 2 and the wire carries a current of 5.00 A . The density of aluminum is 2.70 g / cm 3 . Formula to calculate the drift speed of the electrons in the wire is, v d = I avg n q A (1) Here, v d is the drift velocity. n is the density of charge carriers. q is the charge on each carrier. A is the cross sectional area. The formula to calculate number of electrons per unit volume is, n = N A V (2) Here, N A is the Avogadro’s number . V is the volume occupied by one mole of aluminum. Formula to calculate the volume occupied by the aluminium is, V = M ρ Here, M is the atomic weight of molecule. ρ is the density of aluminum. The molar mass of the aluminium is 27.05 g / mol . Substitute 27.05 g / mol for M and 2.70 g / cm 3 for ρ in above equation. V = 27.05 g / mol 2.70 g / cm 3 = 10.018 cm 3 / mol ≈ 10.02 cm 3 / mol Thus, the volume occupied by the aluminium is 10.02 cm 3 / mol . Substitute 10.02 cm 3 / mol for V and 6.02 × 10 23 electrons / mole in equation (2). n = 6.02 × 10 23 electrons / mole ( 10.02 cm 3 / mol ) ( 1 × 10 − 2 m 1 cm ) 3 = 0

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ISBN: 9781305804463

Author: Jewett

Publisher: CENGAGE LEARNING - CONSIGNMENT

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Chapter 27, Problem 27.3P

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The drift speed of the electrons in the wire.

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