2300 Final Exam Spring 2001

Name: ______(please print) Signature: ______Circle your class time: 10-11AM, MWF 1-2:30PM, MW 4-5:30PM TuTh DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO ECE 2300 – FINAL EXAM May 2, 2001 5-8PM

1. This exam is open book, open notes. You may use any calculator or computer. Turn all cell phones or other communications devices off. 2. Show all work on these pages. Show all work necessary to complete the problem. If you go on to another page, indicate clearly where your work can be found. A solution without the appropriate work shown will receive no credit. Clearly indicate your answer (for example, by enclosing it in a box). 3. Show all units in solutions, intermediate results, and figures. Units in the exam will be included between square brackets. 4. Use appropriate notations at all times. 5. Do not use red ink. Do not use red pencil. 6. You will have 180 minutes to work on this exam.

1. ______/ 2 2. ______/ 17 3. ______/ 30 4. ______/ 15 5. ______/ 5 6. ______/ 16 ECE 2300 Final Exam – May 2, 2001 – Page 2 of 27

7. ______/ 15 ECE 2300 Final Exam – May 2, 2001 – Page 3 of 27

1) {2 Points} Circle your class time on the front page of this exam. ECE 2300 Final Exam – May 2, 2001 – Page 4 of 27

2) {17 Points} A circuit is made up of resistors and sources. This same circuit is connected to a series of voltmeters, one at a time. First, the circuit is connected to Voltmeter #1 with a meter resistance of 10[k], and a full-scale reading of 50[V], as shown in Figure 1. With this voltmeter connected, the voltage v1 is 22.1[V]. Next, the circuit is connected to Voltmeter #2 with a meter resistance of 20[k], and a full-scale reading of 100[V], as shown in Figure 2. With this voltmeter connected, the voltage v2 is 15.3[V]. Finally, the circuit is connected to a third voltmeter with a meter resistance of 30[k], and a full-scale reading of 150[V]. Find the voltage read by the third voltmeter.

A A Circuit Circuit + +

v Voltmeter v1 Voltmeter 2 #1 #2 - - B B Figure 1 Figure 2 ECE 2300 Final Exam – May 2, 2001 – Page 5 of 27

3) {30 Points} In the circuit shown, switch SW1 was closed and switch SW2 was in position 1 for a long time. Then, switch SW1 was opened at t = 0, and remains open. Then, switch SW2 was moved to position 2 at t = 1[s], and stays there. For the time intervals 0 < t < 1[s], and t > 1[s], calculate the numerical expression for the current iX(t) as defined in the circuit shown. In your expressions, clearly specify the time interval or moment in time for which your expressions apply.

R1=10[kW] t = 0 R2=20[kW] R3=40[kW] SW2 1

SW1 2 C = t = 1[s] 1 R = - + v = 3[mF] 5 i = v = S1 50[kW] S1 S2 100[V] R = 5i 200[V] 4 b + - 100[kW]

iX(t) ib ECE 2300 Final Exam – May 2, 2001 – Page 6 of 27

4) {15 Points} For the following circuit, calculate the numerical expression for the current iX(t). This current is defined in the circuit. Important: For each step in your calculations, show clearly the circuit to which your solution applies.

C1=50[mF] R1=10[W] L1=0.01[H] R3=20[W]

R3= 40[W] + iS vS(t) - L = i (t) 2 X 0.02[H] v( t )= 100cos(2000轾rad t - 30° )[V] S 臌 s iS = 10[A] ECE 2300 Final Exam – May 2, 2001 – Page 7 of 27

5) {5 Points} Find the rms value of the waveform shown below. v(t) 10[V]

0 t in [s] 0 5 7 9 14 16 ECE 2300 Final Exam – May 2, 2001 – Page 8 of 27

6) {16 Points} For the circuit shown, calculate the complex, apparent, average and reactive power delivered by the ideal voltage source to the circuit, and the corresponding power factor.

Z1=10[W] Z2=5j[W] Z3=20[W] Z4=40j[W]

Z5= 50[W] + Vs=100Ð0°[Vrms] Is=5Ð30°[Arms] -

Z6= -100j[W] ECE 2300 Final Exam – May 2, 2001 – Page 9 of 27

7) {15 Points} The load in the figure below absorbs 5[kW] and absorbs 1[kVAR]. The sinusoidal voltage source has a frequency of 60[Hz], and delivers 7.5[kW], but the reactive power delivered by the source is unknown.

a) Find the inductance of the line, LX.

b) Find the expression for the current iX(t).

30[W] LX iX(t)

+ Load

vS(t) -

Source Line Load vS ( t )= 20,000cos(w t )[V] ECE 2300 Final Exam – May 2, 2001 – Page 10 of 27

SOLUTION: 2) {17 Points} A circuit is made up of resistors and sources. This same circuit is connected to a series of voltmeters, one at a time. First, the circuit is connected to Voltmeter #1 with a meter resistance of 10[k], and a full-scale reading of 50[V], as shown in Figure 1. With this voltmeter connected, the voltage v1 is 22.1[V]. Next, the circuit is connected to Voltmeter #2 with a meter resistance of 20[k], and a full-scale reading of 100[V], as shown in Figure 2. With this voltmeter connected, the voltage v2 is 15.3[V]. Finally, the circuit is connected to a third voltmeter with a meter resistance of 30[k], and a full-scale reading of 150[V]. Find the voltage read by the third voltmeter.

A A Circuit Circuit + +

v Voltmeter v1 Voltmeter 2 #1 #2 - - B B Figure 1 Figure 2 ECE 2300 Final Exam – May 2, 2001 – Page 11 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 12 of 27

3) {30 Points} In the circuit shown, switch SW1 was closed and switch SW2 was in position 1 for a long time. Then, switch SW1 was opened at t = 0, and remains open. Then, switch SW2 was moved to position 2 at t = 1[s], and stays there. For the time intervals 0 < t < 1[s], and t > 1[s], calculate the numerical expression for the current iX(t) as defined in the circuit shown. In your expressions, clearly specify the time interval or moment in time for which your expressions apply.

R1=10[kW] t = 0 R2=20[kW] R3=40[kW] SW2 1

SW1 2 C = t = 1[s] 1 R = - + v = 3[mF] 5 i = v = S1 50[kW] S1 S2 100[V] R = 5i 200[V] 4 b + - 100[kW]

iX(t) ib ECE 2300 Final Exam – May 2, 2001 – Page 13 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 14 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 15 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 16 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 17 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 18 of 27

4) {15 Points} For the following circuit, calculate the numerical expression for the current iX(t). This current is defined in the circuit. Important: For each step in your calculations, show clearly the circuit to which your solution applies.

C1=50[mF] R1=10[W] L1=0.01[H] R3=20[W]

R3= 40[W] + iS vS(t) - L = i (t) 2 X 0.02[H] v( t )= 100cos(2000轾rad t - 30° )[V] S 臌 s ECE 2300 Final Exam – May 2, 2001 – Page 19 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 20 of 27

5) {5 Points} Find the rms value of the waveform shown below. v(t) 10[V]

0 t in [s] 0 5 7 9 14 16 ECE 2300 Final Exam – May 2, 2001 – Page 21 of 27

6) {16 Points} For the circuit shown, calculate the complex, apparent, average and reactive power delivered by the ideal voltage source to the circuit, and the corresponding power factor.

Z1=10[W] Z2=5j[W] Z3=20[W] Z4=40j[W]

Z5= 50[W] + Vs=100Ð0°[Vrms] Is=5Ð30°[Arms] -

Z6= -100j[W] ECE 2300 Final Exam – May 2, 2001 – Page 22 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 23 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 24 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 25 of 27

7) {15 Points} The load in the figure below absorbs 5[kW] and absorbs 1[kVAR]. The sinusoidal voltage source has a frequency of 60[Hz], and delivers 7.5[kW], but the reactive power delivered by the source is unknown.

c) Find the inductance of the line, LX.

d) Find the expression for the current iX(t).

30[W] LX iX(t)

+ Load

vS(t) -

Source Line Load vS ( t )= 20,000cos(w t )[V] ECE 2300 Final Exam – May 2, 2001 – Page 26 of 27 ECE 2300 Final Exam – May 2, 2001 – Page 27 of 27