106-20102-MT2 - PROBLEM (1) (25 points) V(V) A copper (Cu)...

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Phys 106 Second Midterm Examination Page 1 Saturday, 07-May, 2011 PROBLEM (1) (25 points) A copper (Cu) wire has a resistance of 40.0 ! at 20.0 °C. An aluminium (Al) wire has three times the length and two times the diameter of the copper wire. Both copper and aluminium have the same temperature coefficient of resistivity of 4.00 " 10 # 3 1 ° C at 20.0 °C. The figure shows a voltage versus current graph for the copper wire. I (A) V (V) 600 300 5.00 10.0 0 0 (a) (5 pts) If the resistivity of copper is 0.600 times that of aluminium, find the resistance of the aluminium wire at 20.0 °C. A wire of length L , radius r and diameter d has a resistance: R = " L # r 2 where r = d 2 . So, the resistance is R = 4 L d 2 . R Al = Al 4 L Al d Al 2 = Cu 0.600 4(3 L Cu ) (4 d Cu 2 ) R Al = 3 2.40 ( Cu 4 L Cu d Cu 2 ) = 3 2.40 (40.0 $ ) R Al = 50.0 " (b) (5 pts) Refer to the given figure and find the resistance of the copper wire when the current in it is 10.0 A. V = IR or R = V I R Cu = 600 V 10.0 A R Cu = 60.0 " (c) (4 pts) Assume that the 10.0-A current in the copper wire is maintained for 1.00 hour. Find the energy delivered to the wire. Energy delivered: E = P " t = I 2 R " t E = (10.0 A) 2 (60.0 " )(3600 s) E = 21.6 " 10 6 J = 21.6 MJ (d) (5 pts) Find the temperature of the copper wire when the current in it is 10.0 A. R = R 0 (1 + # T ) R R 0 = + # T ) " T = 1 ( R R 0 $ 1) = 1 4.00 % 10 $ 3 1 ° C ( 60.0 & 40.0 & $ = 125 ° C " T = T # T 0 = T # 20.0 ° C = 125 ° C T = 145 ° C (e) (6 pts) The copper wire is connected between the terminals of an ideal battery. It is observed that the current increases by a large amount when the wire is immersed in liquid nitrogen at –196 °C. The following sentences are related to the copper wire as it is cooled to –196 °C. Complete each sentence by writing decreases, increases or remains constant for the quantity underlined. Ignore changes in the wire's dimensions. (i) The electric field in the wire . ... (ii) The resistivity of the wire . ...... . . ..
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106-20102-MT2 - PROBLEM (1) (25 points) V(V) A copper (Cu)...

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