pexam2S - Physics 21 Fall 2007 Solution Practice Exam#2...

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Physics 21 Fall, 2007 Solution, Practice Exam #2 Problem 1. For the following circuit, R =8 . 0Ω , L = 2 . 0mH ,and C = 500 µ F, and the frequency is 700 Hz. R L C V rms I rms / ω C I rms R V rms φ ω LI rms (a) (5 pts.) Write the loop equation for this circuit. V IR L dI dt Q C =0 (b) (10 pts.) Draw a phasor diagram for the voltages in this circuit. What is the rms value of the current if V rms =6V? For the phasor diagram shown above, use ωL =2 π × 700 × 0 . 002 H = 8 . 7965 Ω; R =8Ω 1 /ωC = ( 2 π × 700 × 500 × 10 6 F ) 1 . 4547 Ω The resultant vector of ωLI rms and 1 / ( ωC ) I rms is 8.3418 I rms , which points upward. Adding that resultant to I rms R gives V rms = p 8 . 3418 2 +8 2 I rms =11 . 5579 I rms Then V rms =6V=11 . 5579 I rms , so that I rms . 519 A (c) (5 pts.) What is the phase relationship between the current and the applied ac voltage? In other words, does the current lag or lead the applied voltage? by how much? The phase φ is given by tan φ = 8 . 3418 8 φ =46 . 2 . 806 rad . The current lags the applied voltage by 46 . 2 . Problem 2. A single rectangular loop of wire with the di- mensions shown in the ±gure is inside a region of magnetic ±eld B ( t ) directed into the page. The magnitude B ( t )ofthe ±eld is given by B ( t )=0 . 02 t T, where t is in seconds. x x xxxxxxx x x x x x x x x x x x x x x x x 0.4 m 0.8 m (a) (14 pts.) What is the current in the loop at time t =1s if the resistance of the loop is 0.1 Ω? From Faraday’s Law, E = d Φ dt = d dt ³ B ( t ) × 0 . 4m × 0 . 8m ´ = d dt ³ 0 . 02 t × 0 . × 0 . ´ = 0 . 02 × 0 . 4 × 0 . 8=0 . 0064 V Then I = |E| /R . 0064 / 0 . 1=0 . 064 A (b) (6 pts.) In what direction does the current in the loop flow? (Specify clockwise or counterclockwise.) Briefly explain your answer.
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This note was uploaded on 02/29/2008 for the course PHYSICS 21 taught by Professor Hickman during the Spring '08 term at Lehigh University .

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pexam2S - Physics 21 Fall 2007 Solution Practice Exam#2...

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