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Unformatted text preview: saldana (avs387) – hw13 – turner – (56705) 1 This printout should have 17 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points Consider the circuit a b A 31 V 11 V I 1 3 . 7 Ω 4 Ω I 3 5 . 5 Ω I 2 1 . 9 Ω 5 . 9 Ω Find the current through the Amp meter, I 3 . Correct answer: 1 . 08114 A. Explanation: a b A E 1 E 2 I 1 r 1 r 2 I 3 r 3 I 2 r 4 r 5 Let : E 1 = 31 V , E 2 = 11 V , r 1 = 3 . 7 Ω , r 2 = 4 Ω , r 3 = 5 . 5 Ω , r 4 = 1 . 9 Ω , and r 5 = 5 . 9 Ω . We consider R 1 = r 1 + r 2 = 3 . 7 Ω + 4 Ω = 7 . 7 Ω , and R 2 = r 4 + r 5 = 1 . 9 Ω + 5 . 9 Ω = 7 . 8 Ω . From the junction rule, I 1 = I 2 + I 3 . Applying Kirchhoff’s loop rule, we obtain two equations. E 1 − I 1 R 1 − I 3 r 3 = 0 E 1 = I 1 R 1 + I 3 r 3 (1) E 2 − I 3 r 3 + I 2 R 2 = 0 E 2 = I 2 R 2 − I 3 r 3 = ( I 1 − I 3 ) R 2 − I 3 r 3 = I 1 R 2 − I 3 ( R 2 + r 3 ) , (2) Multiplying Eq. (1) by R 2 and Eq. (2) by − R 1 and adding, E 1 R 2 = I 1 R 1 R 2 + I 3 r 3 R 2 (3) −E 2 R 1 = − I 1 R 1 R 2 + I 3 R 1 ( R 2 + r 3 ) (4) E 1 R 2 − E 2 R 1 = I 3 [ r 3 R 2 + R 1 ( R 2 + r 3 )] . Since r 3 R 2 + R 1 ( R 2 + r 3 ) = (7 . 8 Ω) (5 . 5 Ω) +(7 . 7 Ω) (5 . 5 Ω + 7 . 8 Ω) = 145 . 31 Ω , then I 3 = E 1 R 2 − E 2 R 1 r 3 R 2 + R 1 ( R 2 + r 3 ) (5) = (31 V) (7 . 8 Ω) − (11 V) (7 . 7 Ω) 145 . 31 Ω = 1 . 08114 A . 002 (part 2 of 3) 10.0 points Find the current I 1 . Correct answer: 3 . 25373 A. Explanation: From Eq. 1 and I 3 from Eq. 5, we have I 1 = E 1 − I 3 r 3 R 1 = 31 V − (1 . 08114 A) (5 . 5 Ω) 7 . 7 Ω = 3 . 25373 A . 003 (part 3 of 3) 10.0 points Find the current I 2 . saldana (avs387) – hw13 – turner – (56705) 2 Correct answer: 2 . 1726 A. Explanation: From Kirchhoff’s junction rule, I 2 = I 1 − I 3 = 3 . 25373 A − 1 . 08114 A = 2 . 1726 A . 004 (part 1 of 4) 10.0 points An energy plant produces an output potential of 2300 kV and serves a city 189 km away. A highvoltage transmission line carries 780 A to the city. The effective resistance of a trans mission line [wire(s)] is 1 . 56 Ω / km times the distance from the plant to the city. What is the potential provided to the city, i.e. , at the end of the transmission line? Correct answer: 2070 . 02 kV. Explanation: Let : V plant = 2300 kV , ℓ = 189 km , I = 780 A , and ρ = 1 . 56 Ω / km . The potential drop on the wire is V = I R = I ρ ℓ = (780 A) (1 . 56 Ω / km) (189 km) = 229 . 975 kV , so the potential delivered to the city is V city = V plant − V wire = 2300 kV − 229 . 975 kV = 2070 . 02 kV . 005 (part 2 of 4) 10.0 points How much power is dissipated due to resistive losses in the transmission line?...
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 Spring '10
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