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exam2awEq - Physics 21 Fall 2007 1 2 3 4 5 Total Name...

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Physics 21 Fall, 2007 Hour Exam #2 1 2 3 4 5 Total Name: Recitation Time Recitation Leader This exam is closed notes and closed book. You must show enough work on all problems to convince the grader you understand how to solve the problem. You may use a calculator. Give units. There is an equation sheet on the last page. All problems count 20 points. Problem 1. For the following circuit, R = 5 . 0 Ω, L = 40 . 0 mH, and C = 300 nF, and the frequency is 1000 Hz. R L C V rms (a) (5 pts.) Draw a phasor diagram for the voltages in this circuit. What is the rms value of the cur- rent if V rms = 6 V? (b) (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? (c) (5 pts.) What is the power delivered to the circuit by the power supply? (d) (5 pts.) At what frequency would the rms cur- rent be the maximum for the given V rms ? (It is not necessary to derive this result; just show the expression that you use to calculate it.)
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Problem 2. Consider a straight segment of wire of length a carrying a current I . (The rest of the wire need not be considered and is not shown.) P = ( x, 0,0) (0, - a /2,0) (0 ,+a /2,0) x y I d l (a) (5 pts.) Use the Biot-Savart law to write an ex- pression for the magnetic field d B at the point P on the x axis due to the current I in the infinites- imal segment of wire d l located at (0 , y, 0). Sim- plifly your expression by working out the cross product. Be careful to distinguish between the coordinate x and the cross product symbol × . (b) (10 pts.) Find the magnetic field at P due to the current in the finite length of wire from y = a/ 2 to y = + a/ 2. Your answer should be in terms of a , I , and fundamental constants. Remember that B is a vector; include necessary unit vectors.
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