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HW5%20solutions - Physics 204 morning summer 2008 Homework...

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Physics 204, morning summer 2008 Homework 5 solutions Chapter 20 Problems 17,45,55,64 17. REASONING AND SOLUTION Suppose that when the initial temperature of the wire is T 0 the resistance is R 0 , and when the temperature rises to T the resistance is R . The relation between temperature and resistance is given by Equation 20.5 as R = R 0 [1 + α ( T T 0 )], where ° is the temperature coefficient of resistivity. The initial and final resistances are related to the voltage and current as R 0 = V / I 0 and R = V / I , where the voltage V across the wire is the same in both cases. Substituting these values for R 0 and R into Equation 20.5 and solving for T , we arrive at T = T 0 + I 0 I 1 α = 20 ° C + 1.50 A 1.30 A 1 4.5 × 10 4 (C ° ) 1 = 360 ° C 45. SSM REASONING The resistance of one of the wires in the extension cord is given by Equation 20.3: / R L A ρ = , where the resistivity of copper is ρ = 1.72 × 10 8 Ω . m, according to Table 20.1. Since the two wires in the
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