# OHW 14 - terry(ect328 – oldhomework 14 – Turner...

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Unformatted text preview: terry (ect328) – oldhomework 14 – Turner – (59130) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A 3 . 2 g wire has a density of 13 . 5 g / cm 3 and a resistivity of 6 . 2 × 10 − 8 Ω · m. The wire has a resistance of 33 Ω. How long is the wire? Correct answer: 11 . 2323 m. Explanation: Let : m = 3 . 2 g = 0 . 0032 kg , ρ = 13 . 5 g / cm 3 = 13500 kg / m 3 , r = 6 . 2 × 10 − 8 Ω · m , and R = 33 Ω . ρ is density, and r is the resistivity of the wire, so m = ρ V V = m ρ = A ℓ A = m ρ ℓ Thus the resistance is R = r ℓ A = r ℓ m ρ ℓ = r ρ ℓ 2 m ℓ 2 = R m ρ r ℓ = radicalBigg R m ρ r = radicalBigg (33 Ω) (0 . 0032 kg) (13500 kg / m 3 ) (6 . 2 × 10 − 8 Ω · m) = 11 . 2323 m . 002 (part 2 of 2) 10.0 points The wire is made up of atoms with va- lence 4 and molecular mass 63 kg, where u = 1 . 6605 × 10 − 27 kg is the mass of a hy- drogen atom. What is the drift speed of the electrons when there is a voltage drop of 72 . 6 V across the wire? Correct answer: 6 . 40579 × 10 − 5 m / s. Explanation: Let : n con = 4 , m μ = 63 kg , V = 72 . 6 V , N A = 6 . 02 × 10 23 , ρ = 13 . 5 g / cm 3 = 13500 kg / m 3 , ℓ = 11 . 2323 m , and q e = 1 . 602 × 10 − 19 C , where m μ is atomic mass, n con is the num- ber of conduction electrons/atom, and N A is Avogadro’s number. Since the current I is given by I = n q A v d , where n is the density of charge carriers, q the charge on an electron and v d the drift speed, we have v d = I n q e A = V n q e A R . (1) The density of charge carriers is found from knowing how many electrons there are per atom and then the total number of atoms in the wire. The mass of one atom is m μ n A and ρ = m V , so n = n con ρ parenleftbigg m μ N A parenrightbigg = n con ρ N A m μ = (4) (13500 kg / m 3 ) (6 . 02 × 10 23 ) 63 kg = 5 . 16 × 10 26 m − 3 . Since the volume is the cross-sectional area multiplied by the length this tells us that A ℓ = m ρ terry (ect328) – oldhomework 14 – Turner – (59130) 2 A = m ρ ℓ = 63 kg (13500 kg / m 3 ) (11 . 2323 m) = 0 . 000415468 m 2 , v d = V n q e A R (1) = 72 . 6 V 5 . 16 × 10 26 m − 3 × 1 1 . 602 × 10 − 19 C × 1 (0 . 000415468 m 2 )(33 Ω) = 6 . 40579 × 10 − 5 m / s ....
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## This note was uploaded on 02/17/2010 for the course PHY 59130 taught by Professor Turner during the Fall '09 term at University of Texas.

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OHW 14 - terry(ect328 – oldhomework 14 – Turner...

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