EE215, Quiz 3
November 9, 2015
For the first ten minutes of this quiz, you are allowed to discuss the quiz with members of your study/lab
group. During this time, you should have nothing out on your desk except the quiz itself. After the
first ten minutes, you will be given a five minute break to take out a pencil and a basic calculator (that
adds, subtracts, multiplies, and divides ... no graphing, no matrix, no calculus, no wireless functions are
allowed).
After the break, when prompted by your instructor, you may then begin the quiz; you have 35 minutes to
complete it. At 4:20 p.m., you must put your pen, pencil, and calculator away (NO EXCEPTIONS).
You will receive the graded quiz back during quiz section the following week. Illegible answers or
work will not be graded, so please do your best to be neat and methodical in your responses. Likewise,
questions for which you have not shown your work or given some explanation as to how you arrived at the answer(s) will receive no credit.
Good Luck!
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20
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TOTAL
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/100
/60
I have received no help beyond the initial discussion with members of my study group in completing this
quiz and have used only a basic calculator to assist me in completing this quiz. I have abided by UW Academic Honesty policies in preparing for and in completing this quiz.
Signed ___________________________________________________________________________
Print Name (clearly) _________________________________________________________________
Quiz Section (AA, AB, etc…) __________________________________________________________
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Question #1
Write FOUR equations (using mesh analysis) that can be used to directly solve for the current
through the 500 ohm and 700 ohm resistors in the following circuit. Your equations will consist of three mesh equations and one additional equation to solve for the current through the
700 ohm resistor. You must label all voltage polarities and current directions in the circuit to
receive credit for this problem. DO NOT SOLVE these equations.
Solution:
10 - 500Ia - 400 (Ia - Ib) - 200Ia = 0
400 (Ia - Ib) - 600 Ib - 700 (Ib - Ic) = 0
700 (Ib - Ic) - 100 Ic + 20 = 0
I (700 ohm resistor) = Ib - Ic
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Question 2
In the following circuit, find the current i using mesh analysis. You must label all voltage polarities and current directions in the circuit to receive credit for this problem.
Solution:
1.5 - 50Ia - 400Ia - 100 (Ia - Ib) = 0
Ib = -100i
i = Ia
Solving:
i = 0.142mA
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Question #3
Write enough equations to solve for all the currents in the following circuits using mesh analysis. Note that you should have as many equations as you have unknowns and your unknowns
should cover ALL eight currents in this circuit. You must label all voltage polarities and current directions in the circuit to receive credit for this problem. DO NOT SOLVE these equations.
Solution:
Mesh A:
-800Ia - 500 (Ia-Ib) = 0
Supermesh (B and C)
500 (Ia-Ib) - 200 Ib -700 (Ic - Id) - 400 Ib = 0
Ic-Ib = 6mA
Supermesh (D and E)
700 (Ic - Id) - 100Ie = 0
Id - Ie = 8mA
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Question 4
Find the Thevenin Equivalent of the following circuit with respect to the 700 ohm resistor.
Solution:
We can use Method #1 (Successive Source Transformations to reduce this circuit to its
Thevenin Equivalent.
Step 1:
10V source in series with 700 ohm resistance:
Becomes 14.3 mA source in series with 700 ohms
Step 2:
20V soure in series with 100 ohm resistance:
Becomes 200mA source in series with 100 ohm resistance (source pointing downward)
Step 3:
700 ohm resistance from Step 1 is now in parallel with 400 ohm resistance:
Becomes 255 ohm resistor
Step 4:
Transform 14.3 mA source in series with 255 ohm resistance:
3.65V source in series with 255 ohm resistance.
Step 5:
Combine 255 ohm resistance and 600 ohm resistor in series: 855 ohms
Step 6:
Transform 3.65V source in series with 855 ohm resistance
4.27mA source in parallel with 855 ohms (pointing upward)
Step 7:
Combine current source from Step 2 and Current Source from Step 6:
4.27mA - 200mA = 196mA pointing downward in parallel with 855 ohms and 100 ohms
Step 8:
Combine 855 and 100 ohm resistors in parallel: 89.5 ohms
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Step 9:
Transform one more time to get Thevenin Equivalent:
Voltage source is 17.5V in series with 89.5 Ohms
Question 5
Part A
Find the Thevenin Equivalent of the following circuit with respect to the 50 ohm resistor.
Solution: Use Method #2
Find open circuit voltage (replacing 50 ohm resistor with an open circuit):
KVL: 10i -100i - 100i = 0; i = 0. Therefore Voc = 5V
Find the short circuit current (replacing 50 ohm resistor with a short circut):
KVL: 5 - 100i = 0; i = 50mA
KVL: 10i - 100i - 100 * (current through rightmost 100 ohm resistor) = 0
Solving: i (current through right most 100 ohm resistor) = 45 mA flowing right to left.
KCL: Isc = 50mA + 45mA = 95 mA
R(thevenin) = 5/95mA = 52.6 Ohms
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The Thevenin Equivalent is:
Part B
How would you change the value of the 50 Ohm resistors to ensure that maximum power is
transferred to the 50 ohm resistor by this circuit?
Solution:
It would have to be 52.6 ohms for maximum power transfer.
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Extra Work
Please clearly label the problem(s) for which you are showing work on this page.
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