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**Unformatted text preview: **Last Name: ECE 3054
Electrical Theory
Term Test #2 October 30, 2006 1. Read all of these instructions and follow them carefully or 5 points
will be deducted from your grade for each time you do not comply. 2. Your test consists of 2 problems that were selected from a set of 6
problems that cover material since Test # 1. Different students will
have different problem numbers. Each problem is worth 50 points. Work the problems on your paper. Do not write small or crowd
your work and do not write on the back of your paper. 3. You may use one 8 1/2 by 11" sheet of paper with equations and
other information. It may not have problems worked out in any form. It may be written on front and back. Put your name on this and
hand it in with your test. 4. All work on this test is to be your own. You will neither give
nor accept help from any other person. 5. Show all of your work ! Sign the following pledge before turning in your paper. I pledge that the work on this test is totally my own and that I have
neither given nor received help. I pledge that I will not pass information,
in any form, concerning this test to anyone who has not already taken the
test. Print Name Signature Problem # l A. Determine the Thevenin and Norton equivalent circuits for the
following circuit with respect to the load resistor, R1,. Determine the
values of Voc, Isc, and R“, (without using the relationship, R“, = Voc/Isc
except to check your results) for the terminals of RL and draw both the Thevenin and the Norton equivalent circuits IO“ B. Determine the maximum possible power in watts that can be delivered
to the load resistor and the value of RL that will cause maximum power
to be delivered. Set the value of the load resistor equal to 1/z the value that
you determined will result in maximum power transfer and calculate the
power to the load resistor at that value. Problem # 2 A. The linear circuit shown below has a non-linear element that will be
connected to terminals “A” and “B”. The characteristic curve for the
non-linear element was provided by the manufacturer and is attached.
Graphically determine the voltage across and current through the non-
linear element when connected to this circuit. /00 11- B. What value of resistance connected to terminals “A” and “B” would
result in maximum power transfer and what is the value of Pmax in
watts? Problem # 3 {This is not a transient problem) The switch in the circuit below closes at t = 0 and remains closed. 1. Determine the current through and the voltage across each element in
the circuit, including the source, at: 1. The instant the switch closes.
2. After the switch has been closed long enough to reach steady
state. You must ive an ex lanation of how on determined the values. Prior to the switch closing, the current through the inductor is -5 amps
and the voltage across the capacitor is -40 volts with directions and
polarities shown. 3. Calculate the energy stored in the inductor and the capacitor at 14o ~>= J» steady state conditions. Problem # 3 Results Sheet While your calculations and work must be on your own paper, the results
must be recorded below and handed in with your papers. At the instant of time, t = (0+) Vs = Is =
VRI= 1R1:
VR2=_ IR2=
VR3= 1R3:
VL = _ IL =
VC = 10: Vs = _ Is =
VRI= __ IR]:
VR2=_ IR2=
VR3=__ 1R3:
VL = IL = Problem # 4-1 In the following circuit, the switch opens at t = 0. Prior to t = 0, the
current through the inductor is - 10 amps. 1. Write the differential equation needed to solve for IL(t). (You will
need a differential equation in current) 2. Using that differential equation, solve for IL(t)pm, IL(t)¢omp, and
IL(t)complete ‘ 3. Determine the time constant and how long it will take to reach
steady-state conditions. 4. At what time will IL(t) = -5.0a? Problem # 4-2 In the following circuit, the switch closes at t = 0. Prior to t = 0, the
voltage across the capacitor is — 20 volts. /OOV 50x4}: 1. Write the differential equation needed to solve for Vc(t). (You will
need a differential equation in voltage) 2. Using that differential equation, solve for Vc(t)pm, Vc(t)comp, and
Vc(t)complete 3. Determine the time constant and how long it will take to reach
steady-state conditions. 4. At what time will vc (t) = -10.0v? Problem # _5_ l. Solve for the current due to each source acting alone and use those
values to determine the total current IR. 2. Verify you answer by solving for IR with all sources active. Problem # 6 Part A. In the circuit shown below, the voltage source is sinusoidal. Write the
differential equation needed to solve for the voltage across the capacitor. Solve for the particular part of the solution only. This includes determining
the values of all constants. ”36% 20 cos(w“~3
$3 50 Ha Part B. For the R.L,C, circuit shown below, determine the damping ratio and from that determine whether the transient part of the solution for vc(t) will be
over-damped, critically damped, or under-damped. Show all of your work. Write the correct form for the complementary part of vc(t). You do not
need to solve for any of the constants. 171.051. L 3 2N1“
—_/\/\/\,.___rUm—‘ {’0 h
+
C= 5/4.}: 50 v «5:10 ...

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