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fall_07_exam2_sol_phy2049

fall_07_exam2_sol_phy2049 - PHY2049 Fall 2007 Prof Yasu...

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PHY2049 Fall 2007 1 Prof. Yasu Takano Prof. Paul Avery Oct. 17, 2007 Exam 2 Solutions 1. ( WebAssign 26.6 ) A current of 1.5 A flows in a copper wire with radius 1.25 mm. If the cur- rent is uniform, what is the electron drift speed in m/s? Copper has a density of 8960 kg/m 3 , atomic mass of 63.54 and one conduction electron per atom. (1) 2.2 × 10 5 (2) 3.6 × 10 4 (3) 5.4 × 10 3 (4) 7.4 × 10 4 (5) 3.0 × 10 5 The current density j is given by 2 / e d j i r en v π = = , where n e is the conduction electron density and v d is the drift velocity. The electron number density for copper is the same as the atomic den- sity since there is one conduction electron per atom. That calculation gives the electron number density ( ) 3 23 28 0 /10 8960 6.02 10 / 0.06354 8.49 10 e Cu n N A ρ = = × × = × /m 3 , where the factor of 10 3 is the conversion from g to kg in the atomic mass. Using 2 / j i r π = , we obtain v d = 2.2 × 10 5 m/s. 2. ( WebAssign 26.41 ) A heating element is made by maintaining a potential difference of 60.0 V along the length of a Nichrome wire with radius 0.945 mm and a resistivity of 5.00 × 10 7 Ω m. If the element dissipates 5000 W, what is its length in m? (1) 4.0 (2) 5.2 (3) 2.2 (4) 0.56 (5) 0.22 The power dissipated is 2 2 / P i R V R = = , where / R L A ρ = , ρ is the resistivity, L is the length and A = π r 2 is the cross sectional area. Putting in all the numbers yields L = 4.0 m.
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