2b Exam November 13, 2002
ECE 221: Electric Circuits Dr. McNames
Write the first letter in your last name, your 6-digit identification number, and your student identification number below. Do not begin the exam or look at the problems until instructed to do so. You have 100 minutes to complete the exam. Do not use separate scratch paper. If you need more space, use the backs of the exam pages. If you have extra time, double check your answers. If you run out of time, write a note describing your strategy and equations that can be used to help solve the problem.
Problem 1:______ / 15 Problem 2:______ / 17 Problem 3:______ / 18 Total:______ / 50
First Letter in Last Name:_____________ 6-Digit Identification Number:_____________ Student Identification Number:_____________
Exam 2b
ECE 221
Fall 2002
2 of 6
1. Thevenin Equivalents, Norton Equivalents, and Superposition (15 pts) Use the circuit below to answer the following questions. For partial credit, draw the appropriate circuit for each question.
18 V a 6 k 9 k b 6 k 6 k 6 mA
a. (2 pts) Use superposition to find the current that flows from terminal a to b when the terminals are connected (short-circuit) due to the voltage source acting alone.
Iscv = _________ b. (2 pts) User superposition to find the current that flows from terminal a to b when the terminals are connected (short-circuit) due to the current source acting alone.
Isci = _________ c. (1 pt) Find the Norton equivalent current. IN = _________ d. (1 pt) If the current source produced twice as much current as shown, what would the Norton equivalent current be? Hint: linearity. IN,2C = _________ e. (1 pt) If the polarity of the voltage source was reversed, what would the Norton equivalent current be? IN,-V = _________ f. (2 pts) Find the Thevenin/Norton equivalent resistance of the circuit.
Req = _________
Exam 2b
ECE 221
Fall 2002
3 of 6
1. Thevenin Equivalents, Norton Equivalents, and Superposition Continued (15 pts) The circuit on the previous page is repeated below for your convenience.
18 V a 6 k 9 k b 6 k 6 k 6 mA
g. (1 pt) Find the Thevenin equivalent voltage. VTh = _________ h. (2 pts) Draw both the Thevenin and Norton equivalents of the circuit as seen from the nodes a and b. Clearly label these nodes.
i. (1 pt) Suppose a resistor RL is connected to the nodes a and b. What value of RL will maximize the power delivered to RL? RL = __________ j. (1 pt) Suppose a resistor RL is connected to the nodes a and b. What is the maximum power that can be delivered to RL? PL = ___________ k. (1 pt) Is this equal to half of the power produced by the voltage source and current source in the original circuit? (Circle) Yes No
Exam 2b
ECE 221
Fall 2002
4 6
2. of Mesh Current Method (17 points)
1 k
900
ia 3 k
+
0.002 vo
ib
vo
-
2 k
ic
3 mA
id
500
a. (12 pts) Use the mesh-current method to write four independent equations in terms of the currents ia, ib, ic, and id. Do not use any other variables in your equations. If appropriate, use the supermesh technique. You do not need to simplify your equations. Equation 1: Equation 2: Equation 3: Equation 4: b. (4 pts) Solve for the currents ia, ib, ic, and id.
ia =
ib =
ic =
id =
c. (1 pt) How many independent equations would be necessary to solve for the node voltages using the node-voltage technique? n=
Exam 2b
ECE 221
Fall 2002
5 of 6
3. Operational Amplifiers (18 points) Use the circuit below to answer the following questions. The op amp is ideal.
R1 i1 R2 vs R3 R4 vo
a. (1 pt) Does this op amp have negative feedback? (Circle) Yes b. (1 pt) Find i1. i1 = ___________ c. (1 pt) Write an expression for the voltage at the inverting terminal of the op amp in terms of the appropriate resistances and vs. v- = ___________ d. (1 pt) Write an expression for vo in terms of the appropriate resistances and vs. vo = ___________ e. (1 pt) Which resistors affect the relationship of vo and vs? R1 R2 R3 R4 No
f. (1 pt) If we used the real model of an op amp, which resistors would affect the relationship of vo and vs? R1 R2 R3 R4
g. (1 pt) If we used the real model of an op amp and R4 = 0, what would vo be? vo = ___________
Exam 2b
ECE 221
Fall 2002
6 of 6
3. Operational Amplifiers Continued (18 points) Use the circuit below to answer the following questions. The op amps in the circuit are ideal. T...