K. Connor, J. Braunstein - 1 - Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

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 2 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.”

This broadcast event was named an IEEE milestone (with plaque) in 2008.

The radio tower was

destroyed in 1971, but

the base remains in the

Blackman’s Point RV

Park in Brant Rock, MA

K. Connor, J. Braunstein 3 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

Inductance Specs – From Digilent Parts Kit Website

K. Connor, J. Braunstein 4 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

K. Connor, J. Braunstein 5 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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)

K. Connor, J. Braunstein 6 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.

K. Connor, J. Braunstein 7 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.

?

?

?

?

K. Connor, J. Braunstein 8 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.

K. Connor, J. Braunstein 9 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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

mentioned directly or indirectly in the question). R

VI . From this expression a larger R will

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) This question is designed to test your understanding of what happens to source current

and source power when resistors are in series and when resistors are in parallel. All

resistors in the above circuit have the same resistance. All DC voltage sources have the

same voltage.

When considering the above three circuits, in which circuit does the source produce the

largest current? Briefly explain your answer.

_______________________________________________________________

_______________________________________________________________

When Vo is the same for each circuit (for example Vo = 5V), for which circuit does the

source produce the most power?

_______________________________________________________________

_______________________________________________________________

R

R

R R R

R

Circuit BCircuit A Circuit C

Vo Vo Vo

K. Connor, J. Braunstein 10 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

b) This question is designed to test your understanding of square pulse streams. The LT-

Spice generated signal shown above consists of a square voltage pulse. Determine the

frequency of the pulse (Hz) and the duty cycle (%). The vertical scale is 0.6V/Div and the

horizontal scale is 0.3s/Div. Circle the correct answers.

Frequency: 0.8Hz 1.25Hz 1kHz 1MHz

Duty cycle: 0% 25% 75% 100%

c) This question is designed to test your understanding of

current flow in diodes. In the circuit to the right, indicate

which of the following statements is correct.

True / False (circle one)

When the diode is ‘on’, current flows from A to B

d) This question is designed to test your understanding of filters. A sinusoidal source with

5V amplitude is applied to either a low pass filter (LPF) or a high pass filter (HPF). The

filter output voltage is measured at two different frequencies

At 100Hz, Vout has an amplitude of 4.997V

At 1000000Hz, Vout has an amplitude of 0.002V

What type of filter is the circuit?

LPF or HPF (circle one)

e) This question is designed to test your understanding of

inductors and capacitors. As shown to the right, capacitors

and inductors can be approximated as short circuits at certain

frequency ranges. Indicate whether those frequencies are

‘low’ or ‘high’ for the respective components.

Capacitors: ______________

Inductors: ______________

CL

1

2

Short

Circuit

K. Connor, J. Braunstein 11 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

Problem 7 (16 Points) – LC Resonant Circuit

Experiment

The circuit at the right is the same circuit we

studied in classes 5 and 7. The resistance is also

the DC Resistance of the inductor. The pulsed

source is a square wave that is -2V when low,

+1V when high and has a 8ms period with a 50%

duty cycle. The source starts off high (at +1V).

Two complete cycles with (2ms/div, 0.5V/div) of

the Oscillator voltage is shown below.

To make the oscillation easier to see, the scale was expanded to show 200µs/Div during the time

from 3ms to 7.85ms (~8ms). Use the information in the plots to answer the questions below.

a. On the top plot, draw the square wave voltage source. Refer to the opening paragraph for

a description of the source pulse. Pay attention to the Voltage (y) axis values.

b. Approximately, what is the DC resistance of the inductor (R1 in the circuit)?

c. Use the plots to estimate the LC oscillation frequency? Mark the points on the second

plot that you used to make your estimate. Pay attention to the Time (x) axis values.

d. Use the circuit components to calculate the LC oscillation frequency.

e. At t = 4.2ms (shown at the arrow on the second plot), approximately how much energy is

stored in the capacitor?

K. Connor, J. Braunstein 12 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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 0V (ground) 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. For the 555 Timer circuit, which component value should we increase if we want a larger

period, but the same duty cycle? (Circle one)

330Ω 22kΩ 10kΩ 1nF

Resistor Resistor Resistor Capacitor

K. Connor, J. Braunstein - 1 - Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

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 2 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.”

This broadcast event was named an IEEE milestone (with plaque) in 2008.

The radio tower was

destroyed in 1971, but

the base remains in the

Blackman’s Point RV

Park in Brant Rock, MA

K. Connor, J. Braunstein 3 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

Inductance Specs – From Digilent Parts Kit Website

K. Connor, J. Braunstein 4 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

K. Connor, J. Braunstein 5 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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)

K. Connor, J. Braunstein 6 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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)

K. Connor, J. Braunstein 7 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.

?

?

?

?

K. Connor, J. Braunstein 8 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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.

K. Connor, J. Braunstein 9 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

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

mentioned directly or indirectly in the question). R

VI . From this expression a larger R will

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) This question is designed to test your understanding of what happens to source current

and source power when resistors are in series and when resistors are in parallel. All

resistors in the above circuit have the same resistance. All DC voltage sources have the

same voltage.

When considering the above three circuits, in which circuit does the source produce the

smallest current? Briefly explain your answer.

_______________________________________________________________

_______________________________________________________________

When Vo is the same for each circuit (for example Vo = 5V), for which circuit does the

source produce the least power?

_______________________________________________________________

_______________________________________________________________

R

R

R R R

R

Circuit BCircuit A Circuit C

Vo Vo Vo

K. Connor, J. Braunstein 10 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

b) This question is designed to test your understanding of square pulse streams. The LT-

Spice generated signal shown above consists of a square voltage pulse. Determine the

frequency of the pulse (Hz) and the duty cycle (%). The vertical scale is 0.5V/Div and the

horizontal scale is 0.2s/Div. Circle the correct answers.

Frequency: 1Hz 2.5Hz 5Hz 40Hz

Duty cycle: 0% 25% 75% 100%

c) This question is designed to test your understanding of

current flow in diodes. In the circuit to the right, indicate

which of the following statements is correct.

True / False (circle one)

When the diode is ‘on’, current flows from B to A

d) This question is designed to test your understanding of filters. A sinusoidal source with

5V amplitude is applied to either a low pass filter (LPF) or a high pass filter (HPF). The

filter output voltage is measured at two different frequencies

At 100Hz, Vout has an amplitude of 0.002V

At 1000000Hz, Vout has an amplitude of 4.997V

What type of filter is the circuit?

LPF or HPF (circle one)

e) This question is designed to test your understanding of

inductors and capacitors. As shown to the right, capacitors

and inductors can be approximated as open circuits for

certain frequency ranges. Indicate whether those frequencies

are ‘low’ or ‘high’ for the respective components.

Capacitors: ______________

Inductors: ______________

CL

1

2

Open

Circuit

K. Connor, J. Braunstein 11 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

Problem 7 (16 Points) – LC Resonant Circuit

Experiment

The circuit at the right is the same circuit we studied

in classes 5 and 7. The resistance is also the DC

Resistance of the inductor. The pulsed source is a

square wave that is -2V when low, +1V when high

and has a 8ms period with a 50% duty cycle. The

source starts off low (at -2V). Two complete cycles

with (2ms/div, 0.5V/div) of the Oscillator voltage is

shown below.

To make the oscillation easier to see, the scale was expanded to show 500µs/Div during the time

from 7ms to 12ms. Use the information in the plots to answer the questions below.

a. On the top plot, draw the square wave voltage source. Refer to the opening paragraph for

a description of the source pulse. Pay attention to the Voltage (y) axis values.

b. Approximately, what is the DC resistance of the inductor (R1 in the circuit)?

c. Use the plots to estimate the LC oscillation frequency? Mark the points on the second

plot that you used to make your estimate. Pay attention to the Time (x) axis values.

d. Use the circuit component values to calculate the LC oscillation frequency.

e. At t = 8.7ms (shown at the arrow on the second plot), approximately how much energy is

stored in the capacitor?

K. Connor, J. Braunstein 12 Revised: 17 October 2016

Rensselaer Polytechnic Institute Troy, New York, USA

Quiz I Fall 2016

Problem 8 (4 Points) – 555 Timer and Batteries

a. On a 555 Timer chip, in the Astable Multivibrator configuration shown, which pins are

connected together?

For example, you can answer Pins 10 and 12. (Pins 10 and 12 do not exist on the 555

Timer chip).

Pins _______ and _______

Pins _______ and _______

b. For the 555 Timer circuit, if we can only change one component to obtain a larger duty

cycle (the period can change as well) which component value should we increase? (Circle

one)

330Ω 22kΩ 10kΩ 1nF

Resistor Resistor Resistor Capacitor