ee215-w06-exam2s - EE215: Fundamentals of Electrical...

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EE215: Fundamentals of Electrical Engineering Midterm Exam 2 February 22, 2006 Time: in class, 50 minutes Class: _ EE215 _____________ Section: ____________________ Name: ____________________ Student ID: ____________________ Please show all steps in solving the problems. Clearly mark your final answers and don’t forget the units. Problem 1 (10+10+5 points) Suppose you are given an unknown power source that is connected to a potentiometer R with a range from 0 to 1000 Ω (see diagram). You measure the power p dissipated by R and obtain the following curve: 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 R =1000 Ω + V Th R Th ??? p /W R / Ω
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(a) What is the Thévenin equivalent of your power source? Give values for v Th and R Th . (b) Give the equation for the power p as a function of R . (c) What value would p approach if you could make R very large (much larger than 1000 Ω )? Explain your answer. Answer: (a) We recall that maximum power transfer occurs for R = R Th . From the graph we see that the power reaches a maximum of p = 25W for R = 100 Ω . Therefore, R Th = 100 Ω . From p = v 2 / R we can calculate the voltage drop across R as v = pR = 50V. Since R = R Th , v Th is twice this number, thus v Th = 100V. (b) In general, the voltage across R is v = v Th R /( R + R Th ) and the current is i = v Th /( R + R Th ), hence the power is p = vi = v Th 2 R / ( R + R Th ) 2 . In our case, p ( R ) = 10000 R / ( R +100) 2 for R in Ohms and p in Watts. Note:
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ee215-w06-exam2s - EE215: Fundamentals of Electrical...

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