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solutions 9

# solutions 9 - Patel Kinal Homework 9 Due 7:00 pm Inst...

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Patel, Kinal – Homework 9 – Due: Feb 22 2008, 7:00 pm – Inst: Weathers 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 1) 10 points An incandescent bulb has a resistance o± 22 Ω when it is at room temperature (25 C) and 236 Ω when it is hot and delivering light to the room. The temperature coe²cient o± re- sistivity o± the flament is 0 . 007 ( C) - 1 , where the base resistance R 0 is determined at 0 C. What is the temperature o± the bulb when in use? Correct answer: 1657 . 79 C. Explanation: Let : R 1 = 22 Ω , R 2 = 236 Ω , and α = 0 . 007 ( C) - 1 . Temperature dependence o± resistance is R T = R 0 [1 + α ( T - 0 C)] = R 0 [1 + α Δ T ] . (1) Using Eq. (1), at room temperature; e.g. , R 1 = 22 Ω and Δ T 1 = 25 C R 0 = R 1 [1 + α Δ T 1 ] (2) = 22 Ω 1 + [0 . 007 ( C) - 1 ] (25 C) = 18 . 7234 Ω . Using Eq. (1), with resistance R 2 , Δ T 2 = R 2 R 0 - 1 α (3) = 236 Ω 18 . 7234 Ω - 1 0 . 007 ( C) - 1 = 1657 . 79 C . Or directly substituting Eq. (1) into (2), we have Δ T 2 = R 2 R 0 - 1 α = R 2 R 1 [1 + α Δ T 1 ] - 1 α = R 2 + α R 2 Δ T 1 - R 1 α = R 2 - R 1 α R 1 + R 2 R 1 Δ T 1 (4) = 236 Ω - 22 Ω [0 . 007 ( C) - 1 ] (22 Ω) + 236 Ω 22 Ω (25 C) = 1657 . 79 C . keywords: 002 (part 1 o± 4) 10 points An energy plant produces an output poten- tial o± 1400 kV and serves a city 65 km away. A high-voltage transmission line carries 760 A to the city. The e³ective resistance o± a trans- mission line [wire(s)] is 2 . 74 Ω / km times the distance ±rom the plant to the city. What is the potential provided to the city, i.e. , at the end o± the transmission line? Correct answer: 1264 . 64 kV. Explanation: Let : V plant = 1400 kV , = 65 km , I = 760 A , and ρ = 2 . 74 Ω / km . The potential drop on the wire is V = I R = I ρ ‘ = (760 A)(2 . 74 Ω / km)(65 km) = 135 . 356 kV , so the potential delivered to the city is V city = V plant - V wire = 1400 kV - 135 . 356 kV = 1264 . 64 kV .

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Patel, Kinal – Homework 9 – Due: Feb 22 2008, 7:00 pm – Inst: Weathers 2 003 (part 2 of 4) 10 points How much power is dissipated due to resistive losses in the transmission line? Correct answer: 1
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solutions 9 - Patel Kinal Homework 9 Due 7:00 pm Inst...

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