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ECE 307 – Exam 2
Spring 2003
Name (print):
February 13, 2003
This test is closed book and closed notes. SHOW ALL WORK. Partial credit may be given. Work the problems according to the method specified. Be sure to specify whether your answers are in degrees or radians.
1 Phasor Question (25 points)
A sinusoidal voltage with a frequency of (^10002) ∗π Hz, reaches a maximum of 20 volts at t =. 001 seconds. (A) Write an equation of this voltage as a function of time (once with sin and once with cos).
(B) Write this voltage as a phasor. (once with an RMS value and once with the peak value)
(C) Now, imagine this voltage was applied across a 1 Farad capacitor, what would the current that flows through the capacitor be? (give the answer as a phasor as well as a function of time).
2 Phasor Question (25 points)
The voltage v(t) is given as v(t) = 10cos(1000t) + 12cos(1000t + 45◦) + 20sin(1000t). (A) Express v(t) as a phasor. (give answer using peak magnitude)
(B) Give the answer to part (A) in rectangular form.
(C) Computer the RMS value of v(t).
V
a
b
R
C I
Figure 2: Circuit.
4 Thevenin’s Equivalent Circuit (25 points)
Determine the Thevenin’s equivalent circuit for this network at the terminals ab. Assume that V = 5cos(10t), R = 10 ohms, C = .01 farads, and I = 1cos(10t − 90 ◦).
5 Extra Credit (5 points)
Imagine a voltage source that produces a perodic voltage where V (t) = 2t^2 , 0 ≤ t ≤ 1. Calculate the RMS value of this periodic waveform.
