pexam1S - Physics 21 Fall, 2007 Solution, Practice Exam #1...

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Unformatted text preview: Physics 21 Fall, 2007 Solution, Practice Exam #1 The graders for the problems were: 1 Belony, 2 Spirko, 3 Noble, 4 La Porta, 5 Rotkin For questions about the grading, see the grader by Oct. 20. Problem 1. 8 3 6 I 3 I 2 I 1 36 V 27 V b a loop 1 loop 2 loop 3 (a) (10 pts.) Write the loop and junction equations needed to determine the currents I 1 , I 2 , and I 3 in the circuit shown. Indicate clearly the loop used to determine each loop equation. The junction and loop equations are: junction: I 1 + I 2 = I 3 loop 1: 27 8 I 3 3 I 1 = 0 loop 2: 36 6 I 2 8 I 3 = 0 loop 3: 36 6 I 2 27 + 3 I 1 = 0 (b) (6 pts.) Determine the currents I 1 , I 2 , and I 3 (including the correct sign) by explicit solution of the equations. You must show your work. We will use loops 1 and 2. First rearrange loop 1, then eliminate I 1 using the junction equation. Then rear- range loop 2. loop 1: 3 I 1 + 8 I 3 = 27 3( I 3 I 2 ) + 8 I 3 = 27 loop 1 : 3 I 2 + 11 I 3 = 27 loop 2: 6 I 2 + 8 I 3 = 36 Divide loop 2 by 2 and add to loop 1 : loop 2 : 3 I 2 + 4 I 3 = 18 loop 1 : 3 I 2 + 11 I 3 = 27 sum: 15 I 3 = 45 I 3 = 3 A Now back substitute to get all the currents: I 1 = 1 A , I 2 = 2 A , I 3 = 3 A (c) (4 pts.) What is the potential difference V b V a between the points marked a and b on the diagram? Use the calculated values of the currents and show how you get your answer. The potential difference can be calculated by any path. Here are two ways to get the answer: V b V a = +36 + 3 I 1 = +6 I 2 + 27 = 39 V . Problem 2. The circular ring of charge shown in the di- agram is in the xy plane centered at the origin and has a radius R . The charge is spread uniformly around the ring with linear density ....
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pexam1S - Physics 21 Fall, 2007 Solution, Practice Exam #1...

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