Name. Draw circuit diagrams for all problems, especially as you simplify the circuits.

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1 Quiz I Spring 2016 Name Part B (80 Points) 1. (10 Pts) 2. (15 Pts) 3. (10 Pts) 4. (10 Pts) 5. (5 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 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. A. Connor, Revised: 3 March 2016 Rensselaer Polytechnic Institute Troy, New York, USA

2 Alexander Graham Bell (March 3, 1847 August 2, 1922) was a Scottish-born scientist, inventor, engineer and innovator who is credited with patenting the first practical telephone. Bell's father, grandfather, and brother had all been associated with work on elocution and speech, and both his mother and wife were deaf, profoundly influencing Bell's life's work. His research on hearing and speech further led him to experiment with hearing devices which eventually culminated in Bell being awarded the first U.S. patent for the telephone in Bell considered his most famous invention an intrusion on his real work as a scientist and refused to have a telephone in his study. Many other inventions marked Bell's later life, including groundbreaking work in optical telecommunications, hydrofoils and aeronautics. Source: Wikipedia 2 March K. A. Connor

3 Inductance Specs From Digilent Parts Kit Website 2 March K. A. Connor

4 2 March K. A. Connor

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 V = 18*21/29 = 13V b. Determine the power delivered to resistor R1. Voltage for this resistor is 5V so power = V 2 /R = 25/8 mw = 3.1mW (anything close to 3mW is fine) Problem 2 (15 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. The two resistors in series in each leg = 3k, taking the two legs in parallel = 1.5kΩ, so V at B is.75*16 = 12V V at C is 1/3 of 12 or 4V V at D is 2/3 of 12 or 8V b. Determine the current through R1. Current through R1 = V at B divided by 3k or 12/3 ma = 4mA All answers check with LT-Spice 2 March K. A. Connor

6 c. The circuit is modified slightly by connecting point C to point D. Determine the voltage at the common point CD. First find R1 R3 = R2 R4 = 1*2/(1+2) kω = 667Ω Then create a simple divider by adding 500 and 667 for the top resistor so that the voltage at CD is 16*667/( ) = 5.8V See below for standard two resistor divider. 2 March K. A. Connor

7 Problem 4 (10 Points) Resistor Ladder Circuit A more complex circuit is formed by essentially connecting a bunch of three resistor voltage dividers in a reasonably symmetric pattern. The voltage source is 42V DC, so that is the voltage at A. The remainder of the circuit is built with two resistor values, 1kΩ and 42kΩ. 43k 43k a. 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? R1 b. What is the approximate value for the parallel combination of two resistors, R1 and R2, when R1 >> R2? R2 b. 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. See circuit. c. Using your modified circuit and the approximations of part a, find the voltages at all nodes (A through G). This will give you reasonable estimates of the actual voltages. Neglect the 43k resistors and we are left with 7 1k resistors in series. Each has the same voltage drop of 6V so the voltages are A: 42, B: 36, C: 30, D: 24, E: 18, F: 12, G: 6 d. Given that the voltages at G, F and E are actually 6.64V, 12.62V and 18.21V, respectively, determine the voltages at nodes B, C and D. The circuit is symmetric so the voltage difference between A and B is the same as that between ground and G. Thus, the voltage at B is = 35.36V. The voltage at C is = 29.38V. The voltage at D is = 23.79V. Answers check with results from LT-Spice. 2 March K. A. Connor

8 Problem 4 (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 33V 2 100kΩ 32.99V 3 10kΩ 32.96V 4 1kΩ 32.64V 5 100Ω 29.73V 6 10Ω 15.71V 7 1Ω 2.75V a. Determine the source voltage Vsource. 33V because 1MΩ is very large so it is, in effect, an open circuit load. b. Determine the source resistance Rsource. Pick any of the smaller loads because the voltage has dropped by at least half. For trial 6, = 33*10/(10+R) then solve for R to get 11Ω. Check the answer to be sure and = 33*10/21 Problem 5 (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. Either 1+ (orange) or 2+ (blue) at OUT and 1- (orange-white) or 2- (blue-white) at ground.?? 2 March K. A. Connor

9 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? 2 March K. A. Connor

10 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 2 March K. A. Connor

11 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? Period = 8ms so 125Hz b. What is the frequency of the damped oscillation voltage? Hint: Can be found 2 ways. Period = 200µs so 5kHz c. What is the value of the capacitance? Hint: The capacitor value is not standard. ω=1/sqrt(lc) so C =.3µF d. What is the value of the resistance? Hint: The inductor is a standard component. From page 4, 9 Ohms 2 March K. A. Connor

12 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? From page 4, 18 Ohms 2 March K. A. Connor