An aluminum wire carrying a current of 3.0 A has a cross-sectional area of 6.0 1

Question

An aluminum wire carrying a current of 3.0 A has a cross-sectional area of 6.0 10-6 m2. Find the drift speed of the electrons in the wire. The density of aluminum is 2.7 g/cm3. (Assume that one electron is supplied by each atom.)
________m/s

Explanation / Answer

nswer ... 34.9 cm / s ... … I = ?Q / ?t … --> … ?Q = I ?t … … ?Q = e N = e n A [ u ?t ] … n = number of electrons per unit volume … … number of electrons in volume V = number of moles of Al in V … … density ? = 2.7 g / cm ³ … --> … 2.7 g in 1.0 cm ³ = 2.7 g in ( 1.0 × 10 ?³ L ) ... … n = 2.7 g / ( 27 g / mol ) = 0.1 mol …using ratio and proportion … … 1 mol / 22.4 L = 0.1 mol / V … --> … V = ( 0.1 ) ( 22.4 L ) = 2.24 L … … molar density ?0 = ( 0.1 mol ) / ( 2.24 L ) = 0.04464 mol / L …………………….. = 0.04464 mol / 1000 cm ³ = 4.464 × 10 ?5 mol / cm ³ ... … mass in moles m0 = ?0 V = ?0 [ A ( u ?t ) ] = ( 4.464 × 10 ?5 ) [ A ( u ?t ) ] … Using ratio and proportion again … … 1 mol / 6.02 × 10 ²³ = ( 4.464 × 10 ?5 ) [ A ( u ?t ) ] / N … … N = ( 6.02 × 10 ²³ ) ( 4.464 × 10 ?5 ) [ A ( u ?t ) ] …… = ( 2. 687 × 10 ¹? ) [ A ( u ?t ) ] …

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