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**Unformatted text preview: **Last Name: ECE 3054
Electrical Theory
Term Test #2 October 29, 2007 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 8
problems that cover material since Test # 1. Different students will
have different problem numbers. Each problem is worth 50 points. Work the problems on the paper provided. Do not write small or crowd your work and do not write on the back of any paper. 3. You may use one 8 1/2 by 11" sheet of paper with equations and
other information. It may not have sample problems worked out in any
form and it may not have any circuits drawn on it. 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 # 1 Use mesh-current analysis to solve for the mesh—currents in the circuit
shown below. You must use the mesh-currents as deﬁned in the circuit diagram. B. Use the mesh currents to determine the voltage across and current
through the dependent source. Problem # 2 A. Determine the Thevenin and Norton equivalent circuits for the
following circuit with respect to the load resistor, RL. Determine the values of Voc, Isc, and R... for the terminals of RL (without using the
relationship, R“. = Voc/Ise except to check your results.) You must
calculate each value independent of the other two. Draw both the
Thevenin and the Norton equivalent circuits 15-9- /0-0- ,0” 0 303- 20-“. Elva“; 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 # 3 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 clement when connected to this circuit. I511- Ion. 20a. 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? s 3. 2%, >9» son, . $3“ , >3 0 :. «MG 65x. , ~
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H — Okmﬁukuqﬁfﬂv Con 2249;” Problem # 4 (This is not a transient problem) The switch in the circuit below closes at t = 0 and remains closed. 1. Determine the following voltages and currents: 1. At the instant the switch closes, determine the values of V1, VL, Is and lo.
2. After the switch has been closed long enough to reach steady state, determine 15, IL, and Vc. You must show all of your work. Prior to the switch closing, the current through the inductor is -5 amps
and the voltage across the capacitor is —80 volts with directions and
polarities shown. I 3. Calculate the energy stored in the inductor and the capacitor at steady state conditions. \/
+ l 5-“- 10-9- Problem # 5 In the following circuit, the switch closes at t = 0. Prior to t = 0, the
current through the inductor is —- 50 ma. +70 500 IL /Ov 11109 = “ 50m? 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)mmp, and
IL(t)complcte 3. Determine the time constant and how long it will take to reach
steady—state conditions. 4. At what time will IL(t) = -20ma? Problem # 6 In the following circuit, the switch opens at t = 0. Prior to t = 0, the
voltage across the capacitor is —— 5 volts. 1. Write the differential equation needed to solve for Vc(t). (Y on will
need a differential equation in voltage) 2. Using that differential equation, solve for Vc(t)pm, Vc(t)mp, and
Vc(t)eompmeM 3. Determine the time constant and how long it will take to reach
steady-state conditions. 4. At what time will Vc (t) = -1v? Problem # 7 Use the superposition theorem to determine the value of IR. 15‘- if; /0v 9 6"" 9 W)" 1. 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 In with all sources active. Problem # 8 Part A. In the circuit shown below, the voltage source is sinusoidal. Write the
differential equation needed to solve for the current through the
inductor. Solve for the particular part of the solution only. This
includes determining the values of all constants. 50-9— L= /OOMH 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. 4w) 2 3 C05 (37%) ...

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