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ECE 2201 – Final ExamDecember 7, 2016

Keep this exam closed until you are told to begin.

1. This exam is closed book, closed notes. You may use one 8.5” x 11” crib sheet, or its equivalent.2. Show all work on these pages. Show all work necessary to complete the problem. A solution without the appropriate work shown will receive no credit. A solution that is not given in a reasonable order will lose credit. Clearly indicate your answer (for example by enclosing it in a box).3. It is assumed that your work will begin on the same page as the problem statement. If you choose to begin your work on another page, you must indicate this on the page with the problem statement, with a clear indication of where the work can be found. If your work continues on to another page, indicate clearly where your work can be found. Failure to indicate this clearly will result in a loss of credit. 4. Show all units in solutions, intermediate results, and figures. Units in the exam will be included between square brackets.5. Do not use red ink. Do not use red pencil.6. You will have 170 minutes to work on this exam.

1. ________________/30

2. ________________/35

3. ________________/35

4. ________________/35

5. ________________/35

6. ________________/30

Total = 200

ECE 2201 – Final Exam – December 7, 2016 – Page 2

Room for extra work

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1. {30 Points} Use the node-voltage method to write a complete set of equations that could be used to solve this circuit. Do not simplify the circuit. Do not attempt to simplify or solve your equations. Define all variables clearly.

vX

60[Ω]iW

70vW

40[S]vY

iW+

50iX

_+

+_

+ _+_

+_ _

vW

vY

iX

8[Ω]

26[Ω]

32[Ω]

_+

+ _

+ _6[A]

7[Ω]

9[Ω]10[Ω]

4[Ω]

11[Ω]

12[Ω]

13[V]

14[Ω]

15[V]16[Ω]

17[Ω]

18[Ω] 19[Ω]20[Ω] 21[Ω]

22[Ω]

23[A]

24[Ω]

25[Ω]

5[A]

27[Ω]

28[Ω]

30[V] 34[V]

35[Ω]3[Ω]

36[Ω]

iY

42[A]

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Room for extra work

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2. {35 Points} A device can be modeled as a current source in parallel with a resistance. This device is shown in Figure 1. This device is connected to the circuit shown in Figure 2.a) Find the equivalent resistance seen by the Device in Figure 2.b) Find the power absorbed by the device in Figure 2.

8.6[A] 1.5[Ω]

K

L

Figure 1

Device

1.0[Ω]

1.2[Ω]

1.6[Ω]

2.4[Ω]

5.6[Ω]6.8[Ω]

3.3[Ω]6.2[Ω]

9.1[Ω]

5.1[Ω]

8.2[Ω] 7.5[Ω]

4.3[Ω]

3[Ω]

3.9[Ω]

4.7[Ω]

3.6[Ω]

2.4[Ω]

KL

Figure 2

ECE 2201 – Final Exam – December 7, 2016 – Page 6

Room for extra work

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3. {35 Points} Use the circuit below to solve this problem. For your solution, do not use the Node-Voltage Method or the Mesh-Current Method and apply source transformation theorem at least twice. The power delivered by the 3[A] current source is 28.2[W]. Find RC. Show your steps in a clear fashion. For the voltage dependent current source, the units for the number 3 is [S], that is 3[S]vX.

+_

+_

+ _6.8[Ω]

7.5[Ω]

5[A]

9.1[Ω]24[V]

3.9[Ω]0.5[Ω]iX

3vX

4.7[Ω]

2.7[Ω]

iX

2[Ω]

3[A]

4V]

2.2[Ω]

11[Ω] ܴ�

+ _vX

ECE 2201 – Final Exam – December 7, 2016 – Page 8

Room for extra work

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4. {35 Points} The device shown in Figure 1 can be modeled as an ideal current source in parallel with a resistance. The relationship between the voltage across the device and the current through the device is shown in Figure 2. This device is connected to a circuit as shown in Figure 3.a) Find a model for the device, and draw it, showing terminals a and b. In the

drawing, show the numerical values of the components.b) Two identical versions of the device are connected in the circuit in Figure 3.

Note the positions of terminals a and b for each of the devices. Find vX in this circuit.

ECE 2201 – Final Exam – December 7, 2016 – Page 10

Room for extra work

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5. {35 Points} Use the circuit below to solve this circuit.a) Find the Thevenin Equivalent as seen by the vS1 voltage source. Draw the

equivalent and attach the vS1 voltage source. In the drawing, show the numerical values of the components.

b) Find the power delivered by the vS1 voltage source in the circuit below.

ECE 2201 – Final Exam – December 7, 2016 – Page 12

Room for extra work

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6. {30 Points} Use superposition in the circuit below to find vQ.

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SOLUTIONS1. {30 Points} Use the node-voltage method to write a complete set of equations that could be used to solve this circuit. Do not simplify the circuit. Do not attempt to simplify or solve your equations. Define all variables clearly.

ECE 2201 – Final Exam – December 7, 2016 – Page 15

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2. {35 Points} A device can be modeled as a current source in parallel with a resistance. This device is shown in Figure 1. This device is connected to the circuit shown in Figure 2.a) Find the equivalent resistance seen by the Device in Figure 2.b) Find the power absorbed by the device in Figure 2.

8.6[A] 1.5[Ω]

K

L

Figure 1

ECE 2201 – Final Exam – December 7, 2016 – Page 17

ECE 2201 – Final Exam – December 7, 2016 – Page 18

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3. {35 Points} Use the circuit below to solve this problem. For your solution, do not use the Node-Voltage Method or the Mesh-Current Method and apply source transformation theorem at least twice. The power delivered by the 3[A] current source is 28.2[W]. Find RC. Show your steps in a clear fashion. For the voltage dependent current source, the units for the number 3 is [S], that is 3[S]vX.

ECE 2201 – Final Exam – December 7, 2016 – Page 20

ECE 2201 – Final Exam – December 7, 2016 – Page 21

4. {35 Points} The device shown in Figure 1 can be modeled as an ideal current source in parallel with a resistance. The relationship between the voltage across the device and the current through the device is shown in Figure 2. This device is connected to a circuit as shown in Figure 3.a) Find a model for the device, and draw it, showing terminals a and b. In the

drawing, show the numerical values of the components.b) Two identical versions of the device are connected in the circuit in Figure 3.

Note the positions of terminals a and b for each of the devices. Find vX in this circuit.

ECE 2201 – Final Exam – December 7, 2016 – Page 22

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ECE 2201 – Final Exam – December 7, 2016 – Page 24

5. {35 Points} Use the circuit below to solve this circuit.a) Find the Thevenin Equivalent as seen by the vS1 voltage source. Draw the

equivalent and attach the vS1 voltage source. In the drawing, show the numerical values of the components.

b) Find the power delivered by the vS1 voltage source in the circuit below.

ECE 2201 – Final Exam – December 7, 2016 – Page 25

ECE 2201 – Final Exam – December 7, 2016 – Page 26

6. {30 Points} Use superposition in the circuit below to find vQ.

ECE 2201 – Final Exam – December 7, 2016 – Page 27