Name Section 1 (12 1:50PM, Monday and Thursday) Draw circuit diagrams for all problems, especially as you simplify the circuits.

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1 Quiz I Fall 2016 Name Section 1 (12 1:50PM, Monday and Thursday) Part B (80 Points) 1. (10 Pts) 2. (16 Pts) 3. (10 Pts) 4. (5 Pts) 5. (9 Pts) 6. (10 Pts) 7. (16 Pts) 8. (4 Pts) Total Draw circuit diagrams for all problems, especially as you simplify the circuits. Be sure to fully annotate plots, even when the problem does not ask you to do this. Show all of your work. Use the backs of pages if there is not enough room on the front. Almost all problems can be solved using more than one method. Check your answers by using a second method. At least skim through the entire quiz before you begin and then start with the problems you know best. The proctor will only answer clarification questions where wording is unclear or where there may be errors/typos. No other questions will be responded to. K. Connor, J. Braunstein Revised: 17 October 2016 Rensselaer Polytechnic Institute Troy, New York, USA

Reginald Fessenden (October 6, 1866 July 22, 1932) was a Canadian inventor who performed pioneering experiments in radio, including the use of continuous waves and the early maybe the first radio

As reported by the Museum of Radio and Technology: For their entire careers, the Sparks, the ship wireless operators for the United Fruit Company, along with the US Navy, had only heard Morse code

Suddenly they heard something that made some think they were dreaming, a human voice coming from those headphones. Then they heard singing. There was a violin solo. Then a man made a speech.

2 Reginald Fessenden (October 6, 1866 July 22, 1932) was a Canadian inventor who performed pioneering experiments in radio, including the use of continuous waves and the early maybe the first radio transmissions of voice and music. In his later career he received hundreds of patents for devices in fields such as high-powered transmitting, sonar, and television. As reported by the Museum of Radio and Technology: For their entire careers, the Sparks, the ship wireless operators for the United Fruit Company, along with the US Navy, had only heard Morse code "dit - dahs" coming through their headphones. They had been alerted a few days earlier for a special message to come at 9 PM Eastern Time on Christmas Eve (1906). Suddenly they heard something that made some think they were dreaming, a human voice coming from those headphones. Then they heard singing. There was a violin solo. Then a man made a speech. Some called their captain and ship's officers to come and listen. The genius responsible was Reginald Fessenden. He had succeeded in transmitting voice and music over the air. Fessenden himself played a violin solo of O Holy Night accompanying himself as he sang the last verse. He also read the Biblical account of the birth of Christ from Luke chapter 2 over the air. The text of the angels' song Glory to God in the Highest - and on Earth - Peace to Men of Goodwill was heard as if by miracle. At the conclusion, Fessenden wished all a Merry Christmas and invited the Sparks to write him at Brant Rock, Massachusetts with reception reports. Reports were received from ships along the Atlantic northeast coast and from shore stations as far south as Norfolk, Virginia. A repeat broadcast on New Year's Eve was heard as far south as the West Indies. The radio tower was destroyed in 1971, but the base remains in the Blackman s Point RV Park in Brant Rock, MA This broadcast event was named an IEEE milestone (with plaque) in October K. Connor, J. Braunstein

3 Inductance Specs From Digilent Parts Kit Website 1 October K. Connor, J. Braunstein

4 1 October K. Connor, J. Braunstein

5 Problem 1 (10 Points) Basic Voltage Divider A voltage divider consisting of two resistors and a DC voltage source is configured as shown. a. Determine the output voltage across R2 (in Volts) b. Determine the power delivered to resistor R1 (in milli- Watts) Problem 2 (16 Points) A Bit More Complicated Voltage Divider A somewhat more complicated voltage divider, consisting of more than the usual two resistors and DC source, is configured as shown. a. Determine the voltages at B and D (in Volts) b. Determine the current through R5 (in ma) 1 October K. Connor, J. Braunstein

6 The circuit is modified by replacing the 12kΩ resistors R3 and R2 with 1.2MΩ and the 1kΩ resistor R5 with 4kΩ. c. Determine the voltages at B and D. d. Determine the current through R5. 1 October K. Connor, J. Braunstein

7 Problem 3 (10 Points) Source Characterization Using a Voltage Divider Batteries and other voltage sources can generally be modeled by combining an ideal voltage source and a resistor. The circuit at the right is set up to study some kind of a black box DC voltage source. Six different load resistors are connected and the voltage V(OUT) is measured. The results of the six trials are listed in the table below. Note that there is more information than you need to find the source voltage and resistance.?? Trial Rload V(OUT) 1 1MΩ 110.9V 2 100kΩ 110.3V 3 10kΩ 104.1V 4 1kΩ 66.6V 5 100Ω 14.5V 6 10Ω 1.6V 7 1Ω 0.2V a. Determine the source voltage Vsource (in Volts) b. Determine the source resistance Rsource (in Ohms) Problem 4 (5 Points) Measurements The black box circuit from the previous problem is redrawn at the right (with the box outline shown). What wires from your Analog Discovery board should be connected to this circuit (and where) to obtain the voltage information in the table? List the wires below and show their connection points on the circuit diagram. There is more than one correct answer.?? 1 October K. Connor, J. Braunstein

8 Problem 5 (9 Points) Resistor Ladder Circuit A more complex circuit is formed by essentially connecting a bunch of voltage dividers. The voltage source is 84V DC, so that is the voltage at A. The remainder of the circuit is built with resistor values, 1kΩ, 2kΩ and 40kΩ. a. (2 pts) Before beginning the analysis of this circuit, answer the following two general questions: a. What is the approximate value for the series combination of two resistors, R1 and R2, when R1 >> R2? b. What is the approximate value for the parallel combination of two resistors, R1 and R2, when R1 >> R2? b. (2 pts) The circuit above was designed without checking to be sure the resistor values chosen were standard values. Check the values selected and change any non-standard values to the closest standard value and indicate the changes on the circuit diagram. c. (3 pts) Using your modified circuit and the approximations of part a, find the voltages at nodes B, C, D. This will give you reasonable estimates of the actual voltages. d. (2 pts) Assume that you were able to measure the actual voltages only at nodes B and C and found them to be 68.0V and 39.6V, respectively. Determine the voltage at node D. Compare the three actual voltages to your approximate calculations. 1 October K. Connor, J. Braunstein

9 1 October K. Connor, J. Braunstein

10 Problem 6 (10 Points) Conceptual Questions This problem contains some conceptual questions. The following addresses how to approach such questions, provided in the unlikely event that you have not seen such questions before. A conceptual question is designed to help determine whether a student has an accurate working knowledge of a specific set of concepts. For example, from the background quiz you completed on the first day of class: A 9V battery is connected across a 2kΩ resistor. If the resistor is replaced with a 10kΩ resistor, will the current from the battery a. Increase b. Decrease c. Stay about the same This question tests conceptual knowledge of Ohm s Law. It can most rigorously be answered by recalling the relationship between voltage, current and resistance (the three parameters V mentioned directly or indirectly in the question). I. From this expression a larger R will R produce a smaller I for the same voltage (9V in this case). The answer does not depend on the exact values of the two resistances, only that a resistor is replaced with one that is larger. Then the current will be smaller, so the answer is b. Decrease. Conceptual Questions: The answers for all questions are worth (2 pts) each, except where noted. Remember to briefly explain your answers. a) Is the image shown at the right 1. A short circuit? 2. An open circuit? b) Is the image shown at the right 1. A short circuit? 2. An open circuit? 1 October K. Connor, J. Braunstein

11 c) In the standard voltage divider configuration shown at the right, resistor R1 is much larger than resistor R2. Is the power dissipated in R1 1. Much greater than the power dissipated in R2 2. Much less than the power dissipated in R2 3. About the same as the power dissipated in R2 d) In the circuit at the right, two resistors (R1 much larger than R2) are connected in parallel across a voltage source V. Is the power dissipated in R1 1. Much greater than the power dissipated in R2 2. Much less than the power dissipated in R2 3. About the same as the power dissipated in R2 e) The LT-Spice generated signal shown above consists of two sinusoidal voltage waves with different frequencies. What are the two frequencies? The vertical scale is 100mV/Div and the horizontal scale is 0.3ms/Div. Circle the correct answers. 500Hz 1kHz 2kHz 2.5kHz 5kHz 10kHz 20kHz 25kHz 1 October K. Connor, J. Braunstein

12 Problem 7 (16 Points) LC Resonant Circuit Experiment The circuit at the right is similar to the one we studied in classes 5 and 7. A different inductor (L is given) and a different capacitor (C is unknown) are used. The resistance is also the DC Resistance of the inductor (also not given in the figure). The pulsed source is a square wave that is -3V when low and +1V when high. Two complete cycles of the Source and Oscillator voltages are shown below. The time scale is 2ms/Div and the voltage scale is 0.5V/Div. Recall that there are 10 divisions both horizontally and vertically.?? To make the oscillation easier to see, the scale was expanded to show 200µs/Div during the time from 8mss to 12ms. Use the information in plots to answer the following: a. What is the frequency of the Source square wave voltage? b. What is the frequency of the damped oscillation voltage? Hint: Can be found 2 ways. c. What is the value of the capacitance? Hint: The capacitor value is not standard. d. What is the value of the resistance? Hint: The inductor is a standard component. 1 October K. Connor, J. Braunstein

13 Problem 8 (4 Points) 555 Timer and Batteries a. On a 555 Timer chip, in the Astable Multivibrator configuration shown, what pins do we connect the +9V from the battery to? Circle all correct answers. 1. Pin 1 2. Pin 2 3. Pin 3 4. Pin 4 5. Pin 5 6. Pin 6 7. Pin 7 8. Pin 8 b. What is a typical internal resistance for a 9V Lithium battery? 1 October K. Connor, J. Braunstein

14 Quiz I Fall 2016 Name Section 2 (4 5:50PM, Monday and Thursday) Part B (80 Points) 1. (10 Pts) 2. (16 Pts) 3. (10 Pts) 4. (5 Pts) 5. (9 Pts) 6. (10 Pts) 7. (16 Pts) 8. (4 Pts) Total Draw circuit diagrams for all problems, especially as you simplify the circuits. Be sure to fully annotate plots, even when the problem does not ask you to do this. Show all of your work. Use the backs of pages if there is not enough room on the front. Almost all problems can be solved using more than one method. Check your answers by using a second method. At least skim through the entire quiz before you begin and then start with the problems you know best. The proctor will only answer clarification questions where wording is unclear or where there may be errors/typos. No other questions will be responded to. K. Connor, J. Braunstein Revised: 17 October 2016 Rensselaer Polytechnic Institute Troy, New York, USA

15 Reginald Fessenden (October 6, 1866 July 22, 1932) was a Canadian inventor who performed pioneering experiments in radio, including the use of continuous waves and the early maybe the first radio transmissions of voice and music. In his later career he received hundreds of patents for devices in fields such as high-powered transmitting, sonar, and television. As reported by the Museum of Radio and Technology: For their entire careers, the Sparks, the ship wireless operators for the United Fruit Company, along with the US Navy, had only heard Morse code "dit - dahs" coming through their headphones. They had been alerted a few days earlier for a special message to come at 9 PM Eastern Time on Christmas Eve (1906). Suddenly they heard something that made some think they were dreaming, a human voice coming from those headphones. Then they heard singing. There was a violin solo. Then a man made a speech. Some called their captain and ship's officers to come and listen. The genius responsible was Reginald Fessenden. He had succeeded in transmitting voice and music over the air. Fessenden himself played a violin solo of O Holy Night accompanying himself as he sang the last verse. He also read the Biblical account of the birth of Christ from Luke chapter 2 over the air. The text of the angels' song Glory to God in the Highest - and on Earth - Peace to Men of Goodwill was heard as if by miracle. At the conclusion, Fessenden wished all a Merry Christmas and invited the Sparks to write him at Brant Rock, Massachusetts with reception reports. Reports were received from ships along the Atlantic northeast coast and from shore stations as far south as Norfolk, Virginia. A repeat broadcast on New Year's Eve was heard as far south as the West Indies. The radio tower was destroyed in 1971, but the base remains in the Blackman s Point RV Park in Brant Rock, MA This broadcast event was named an IEEE milestone (with plaque) in October K. Connor, J. Braunstein

16 Inductance Specs From Digilent Parts Kit Website 1 October K. Connor, J. Braunstein

17 1 October K. Connor, J. Braunstein

18 Problem 1 (10 Points) Basic Voltage Divider A voltage divider consisting of two resistors and a DC voltage source is configured as shown. a. Determine the output voltage across R2 (in Volts) b. Determine the power delivered to the load R2 (in milli- Watts) Problem 2 (16 Points) A Bit More Complicated Voltage Divider A somewhat more complicated voltage divider, consisting of more than the usual two resistors and DC source, is configured as shown. a. Determine the voltages at B and D (in Volts) b. Determine the current through R5 (in milli-amps) 1 October K. Connor, J. Braunstein

19 The circuit is modified by replacing the 6kΩ resistors R3 and R2 with 600kΩ and the 1kΩ resistor R5 with 1.5kΩ. c. Determine the voltages at B and D (in Volts) d. Determine the current through R5 (in milli-amps) 1 October K. Connor, J. Braunstein

20 Problem 3 (10 Points) Source Characterization Using a Voltage Divider Batteries and other voltage sources can generally be modeled by combining an ideal voltage source and a resistor. The circuit at the right is set up to study some kind of a black box DC voltage source. Six different load resistors are connected and the voltage V(OUT) is measured. The results of the six trials are listed in the table below. Note that there is more information than you need to find the source voltage and resistance.?? Trial Rload V(OUT) 1 1MΩ 98.9V 2 100kΩ 98.7V 3 10kΩ 95.8V 4 1kΩ 74.3V 5 100Ω 22.9V 6 10Ω 2.9V 7 1Ω 0.3V a. Determine the source voltage Vsource (in Volts) b. Determine the source resistance Rsource (in Ohms) Problem 4 (5 Points) Measurements The black box circuit from the previous problem is redrawn at the right (with the box outline shown). What wires from your Analog Discovery board should be connected to this circuit (and where) to obtain the voltage information in the table? List the wires below and show their connection points on the circuit diagram. There is more than one correct answer.?? 1 October K. Connor, J. Braunstein

21 Problem 5 (9 Points) Resistor Ladder Circuit A more complex circuit is formed by essentially connecting a bunch of voltage dividers. The voltage source is 126V DC, so that is the voltage at A. The remainder of the circuit is built with resistor values: 1kΩ, 2kΩ, 3kΩ and 50kΩ. a. (2 pts) Before beginning the analysis of this circuit, answer the following two general questions: a. What is the approximate value for the series combination of two resistors, R1 and R2, when R1 >> R2? b. What is the approximate value for the parallel combination of two resistors, R1 and R2, when R1 >> R2? b. (2 pts) The circuit above was designed without checking to be sure the resistor values chosen were standard values. Check the values selected and change any non-standard values to the closest standard value and indicate the changes on the circuit diagram. c. (3 pts) Using your modified circuit and the approximations of part a, find the voltages at nodes B, C, D). This will give you reasonable estimates of the actual voltages. d. (2 pts) Assume that you built the circuit and were able to measure the actual voltages only at nodes B and C and (69.1V and 33.9V, respectively). Determine the voltage at node D. Compare the three actual voltages to your approximate calculations. 1 October K. Connor, J. Braunstein

22 1 October K. Connor, J. Braunstein

A conceptual question is designed to help determine whether a student has an accurate working knowledge of a specific set of concepts.

23 Problem 6 (10 Points) Conceptual Questions This problem contains some conceptual questions. The following addresses how to approach such questions, provided in the unlikely event that you have not seen such questions before. A conceptual question is designed to help determine whether a student has an accurate working knowledge of a specific set of concepts. For example, from the background quiz you completed on the first day of class: A 9V battery is connected across a 2kΩ resistor. If the resistor is replaced with a 10kΩ resistor, will the current from the battery a. Increase b. Decrease c. Stay about the same This question tests conceptual knowledge of Ohm s Law. It can most rigorously be answered by recalling the relationship between voltage, current and resistance (the three parameters V mentioned directly or indirectly in the question). I. From this expression a larger R will R produce a smaller I for the same voltage (9V in this case). The answer does not depend on the exact values of the two resistances, only that a resistor is replaced with one that is larger. Then the current will be smaller, so the answer is b. Decrease. Conceptual Questions: The answers for all questions are worth (2 pts) each, except where noted. Remember to briefly explain your answers. a) Is the image shown at the right 1. A short circuit? 2. An open circuit? b) Is the image shown at the right 1. A short circuit? 2. An open circuit? 1 October K. Connor, J. Braunstein

c) In the standard voltage divider configuration shown at the right, resistor R1 is much larger than resistor R2. Is the power dissipated in R1 1. Much greater than the power dissipated in R2 2.

About the same as the power dissipated in R2 d) In the circuit at the right, two resistors (R1 much larger than R2) are connected in parallel across a voltage source V.

24 c) In the standard voltage divider configuration shown at the right, resistor R1 is much larger than resistor R2. Is the power dissipated in R1 1. Much greater than the power dissipated in R2 2. Much less than the power dissipated in R2 3. About the same as the power dissipated in R2 d) In the circuit at the right, two resistors (R1 much larger than R2) are connected in parallel across a voltage source V. Is the power dissipated in R1 1. Much greater than the power dissipated in R2 2. Much less than the power dissipated in R2 3. About the same as the power dissipated in R2 e) The LT-Spice generated signal shown above consists of two sinusoidal voltage waves with different frequencies. What are the two frequencies? The vertical scale is 100mV/Div and the horizontal scale is 0.3ms/Div. Circle the correct answers. 500Hz 1kHz 2kHz 2.5kHz 5kHz 10kHz 20kHz 25kHz 1 October K. Connor, J. Braunstein

25 Problem 7 (16 Points) LC Resonant Circuit Experiment The circuit at the right is similar to the one we studied in classes 5 and 7. A different inductor (L is given) and a different capacitor (C is unknown) are used. The resistance is also the DC Resistance of the inductor (also not given in the figure). The pulsed source is a square wave that is -3V when low and +1V when high. Two complete cycles of the Source and Oscillator voltages are shown below. The time scale is 2ms/Div and the voltage scale is 0.5V/Div. Recall that there are 10 divisions both horizontally and vertically.?? To make the oscillation easier to see, the scale was expanded to show 200µs/Div during the time from 8mss to 12ms. Use the information in plots to answer the following: a. What is the frequency of the Source square wave voltage? b. What is the frequency of the damped oscillation voltage? Hint: Can be found 2 ways. c. What is the value of the capacitance? Hint: The capacitor value is not standard. d. What is the value of the resistance? Hint: The inductor is a standard component. 1 October K. Connor, J. Braunstein

the +9V from the battery to? Circle all correct answers. 1. Pin 1 2. Pin 2 3. Pin 3 4. Pin 4 5.

26 Problem 8 (4 Points) 555 Timer and Batteries a. On a 555 Timer chip, in the Astable Multivibrator configuration shown, what pins do we connect the +9V from the battery to? Circle all correct answers. 1. Pin 1 2. Pin 2 3. Pin 3 4. Pin 4 5. Pin 5 6. Pin 6 7. Pin 7 8. Pin 8 b. What is a typical internal resistance for a 9V Lithium battery? 1 October K. Connor, J. Braunstein

27 Quiz 1 Problem 1, Section 1 V = 24*12/36 = 16V Power to R1 is (24-16) x mw = 5.3mW = (24/36) x (24-16) mw Problem 1, Section 2 V = 12*11/33 = 8V Power to R2 is 8 x.36 mw = 2.9mW = 8 x (12/33) mw Problem 2, Section 1 First Configuration (parts a and b) 12k 4k = 3k; 3k + 3k =6k; VB=36 x (6/9) = 24V; VD = 24 x (1/2) = 12V Current thru R5: 36 / 9 = 4mA

28 Second Configuration (parts c and d) Neglect the large resistors in parallel: VB = 36 x (8/12) = 24V Current thru R5: 36 / 712 = 3mA Problem 2, Section 2 First Configuration (parts a and b) 6k 3k = 2k; 2k + 2k =4k; VB = 25 x 4/5 = 20V; VD = 20 x (1/2) = 10V Current thru R5: 25 / 5 = 5mA Second Configuration (parts c and d)

29 Neglect the large resistors in parallel: VB = 25 x (6/7.5) = 20V Current thru R5: 25 / 7.5 = 3.33mA Problem 3, Section 1 The source voltage and resistance are shown below. For the source voltage, use the largest value of the load resistance, because 1M is very large. We will check it later. Then Vsource = 111V For the resistance, take one of the smaller loads where the voltage is about half of the source. Here we choose 1k and 66.6V. R = (111/66.6) x = 666. We can check another voltage to be sure that these are correct. Choose 100 and 14.5V. R = (111/14.5) x = 666 which checks. Problem 3, Section 2 The source voltage and resistance are shown below

30 For the source voltage, use the largest value of the load resistance, because 1M is very large. We will check it later. Then Vsource = 99V For the resistance, take one of the smaller loads where the voltage is about half of the source. Here we choose 1k and 74.3V. R = (99/74.3) x = 332. We can check another voltage to be sure that these are correct. Choose 100 and 22.9V. R = (99/22.9) x = 332 which checks. The actual answer, as seen above, is 333 Ohms. The accuracy of the numbers in the table give an answer that is off by 1 out of 333, so very, very good. Problem 4, Section 1 & 2 answer. Either 1+ (orange) or 2+ (blue) at OUT and 1- (orange-white) or 2- (blue-white) at ground. Problem 5, Section 1 a. The answer to a is R1, the answer to b is R2. b. The 40k resistor is non-standard. Replace with 39k c. The three voltages are found below. By approximate calculation: VD = 84 x (1/6) = 14V; VC = 84 x (3/6) = 42V; VB = 84 x (5/6) = 70V

31 d. By calculation, the voltage at D is 1/3 the voltage at C: 39.6/3 = 13.2V. The voltages at B, C, and D are all slightly smaller than in the approximate solution because the contribution from the 51k resistor reduces the overall resistance. Problem 5, Section 2 a. The answer to a is R1, the answer to b is R2. b. The 50k resistor is non-standard. Replace with 51k c. The three voltages are found below. By approximate calculation: VD = 126 x (1/7) = 18V; VC = 126 x (2/7) = 36V; VB = 84 x (4/7) = 72V d. By calculation, the voltage at D is ½ the voltage at C: 33.9/2 = 17 (close answers are OK). The voltages at B, C, and D are all slightly smaller than in the approximate solution because the contribution from the 51k resistor reduces the overall resistance.

Name Section 1 (12 1:50PM, Monday and Thursday) Draw circuit diagrams for all problems, especially as you simplify the circuits.

Name Section 1 (12 1:50PM, Monday and Thursday) Part B (80 Points) 1. (10 Pts) 2. (16 Pts) 3. (10 Pts) 4. (5 Pts) 5. (9 Pts) 6. (10 Pts) 7. (16 Pts) 8. (4 Pts) Total Draw circuit diagrams for all problems,