SUNY MARITIME COLLEGE Department of Engineering

ENGR 290 Electrical Engineering I Laboratory Manual August 2012 Prepared by Paul M. Kump

CONTENTS Experiment 1: Verification of Ohm’s Law………………………………………………3 Experiment 2: Resistor Color Codes, Power Dissipation, and Tolerances……………...8 Experiment 3: Verification of Kirchoff’s Laws………………………………………..12 Experiment 4: Voltage and Current Dividers for Series and Parallel Circuits…………15 Experiment 5: The Superposition Principle…………………………………………….20 Experiment 6: Thevenin’s Theorem and Maximum Power Transfer…………………..23 Experiment 7: Measurements of Circuit Transients……………………………………27 Appendix………………………………………………………………………………...30

2

Experiment 1 Verification of Ohm’s Law INTRODUCTION In this experiment, you will learn the correct way to measure voltages, currents, and resistances in an electrical circuit. These new skills will be put to use in verifying Ohm’s Law. OBJECTIVES 1. Investigate how to use a multimeter to measure voltage across a circuit component. 2. Investigate how to use a multimeter to measure current through a circuit component. 3. Investigate how to use a multimeter to measure resistance. 4. Verify Ohm’s Law on a resistor of unknown resistance. Determine the resistance by plotting an I-V curve. MATERIALS DC power supply (1) Multimeter (1) Resistor of unknown resistance (1) 100-Ω resistor (1) PRE-LAB 1. Find the resistor color code in the appendix of this manual. What three colors make up a 100-Ω resistor? Be sure to list the colors in the correct order. 2. Is a resistor a polar component (i.e., does it have specified positive and negative terminals)?

3. How much current is traveling through a 100-Ω resistor that is connected to a 5-V power supply? How much charge has passed through the resistor after 1-μs?

4. If the 100-Ω resistor is rated at 1 watt, what is the maximum voltage that can be applied to this resistor?

3

PART 1 PROCEDURE 1. Set the multimeter to measure DC voltage. 2. Assemble the circuit in Figure 1. Measure the voltage across the resistor, V_R, by placing the multimeter in parallel with the resistor as shown in Figure 2. The voltage may not be the exact value you expect. Enter the value in Table 1. 3. Remove the multimeter and set it to measure current. 4. Measure the current through the resistor, I_R, by placing the multimeter in series with the resistor. You will need to break the circuit as shown in Figure 3. Enter the value in Table 1. Also measure this current in Multisim. 5. Calculate the resistance using Ohm’s Law and your measured voltage and current. Record the value in Table 1. 6. Remove the multimeter and remove the power supply from the circuit. Set the multimeter to measure resistance and measure the resistance of the resistor as shown in Figure 4. Record the value in Table 1.

Figure 1

Figure 2

Figure 3

Figure 4

4

Quantity V_R

Value

Value from Multisim n/a

Units

I_R R (Ohm’s Law)

n/a

R (measured)

n/a Table 1

QUESTIONS (these questions all refer to the hardwire circuit, not the Multisim) 1. Observe how the multimeter was placed in the circuit when measuring voltage. What is the resistance of an ideal voltage meter? Why?

2. Observe how the multimeter was placed in the circuit when measuring current. What is the resistance of an ideal ammeter (current meter)? Why?

3. Why is there a (slight) discrepancy between the measured resistance and the one from Ohm’s Law? Is the problem with Ohm’s Law or something else?

4. What was the percent difference between the current you measured in Multisim and the current you measured in the hardwired circuit?

PART 2 PROCEDURE 1. Set the multimeter to measure current, and construct the circuit in Figure 5 with the unknown resistor.

5

2. Apply the voltages V_R in Table 2, and, for each voltage, record the current through the resistor, I_R. You may have to adjust the range on the multimeter. 3. Plot each set of points (V_R, I_R) on the provided graph paper. Make sure to set the current I_R as the dependent variable (vertical axis) and the voltage V_R as the independent variable (horizontal axis). Label the axes and give your graph a title. 4. On the graph paper, draw in the best-fit line and use it to calculate the unknown resistance. 5. Use the procedure from Part 1 to measure the resistance of the unknown resistor.

Figure 5

V_R (volts) 0

I_R

1 2 3 4 5 6 Table 2 6

QUESTIONS (these questions all refer to the hardwire circuit, not the Multisim) 1. What is the unknown resistance as found with your plot? How did you come up with this number?

2. What is the resistance that you measured with the multimeter?

3. Do the results from Questions 1 and 2 prove Ohm’s Law? Why or why not?

7

Experiment 2 Resistor Color Codes, Power Dissipation, and Tolerances INTRODUCTION This experiment is about measurement of resistance directly and also through voltage and current measurement, with special attention paid to the resistor tolerance and power dissipation. OBJECTIVES 1. 2. 3. 4.

Gain familiarity with resistor color codes. Compare ohmmeter values with voltage-current readings. Observe the power dissipation of resistors. Become familiar with resistor tolerances.

MATERIALS DC power supply (1) Multimeter (1) Assorted resistors (4) 10-Ω resistors (2) PRE-LAB The approximate value of a resistor can be found by the four color bands on it. The nine colors in the sequence are black, brown, red, orange, yellow, green, blue, violet, grey and white. Resistors may have a fifth band that indicates reliability of the resistor. Example: Brown Red Orange Gold: 1 (brown) 2 (red) 10^3 (orange is three)

5% (gold)

= 12kΩ, ±5%

The color code is also given in the appendix. 1. What is the range of possible resistances for a 100-Ω resistor with a 5% tolerance?

2. What is the range of possible resistances for a resistor with color code brown, black, red, gold?

8

3. What is the range of the equivalent resistance of two 10-Ω resistors, each with a 5% tolerance, placed in series? To what percentage tolerance of the equivalent resistance does this range correspond?

4. What is the range of the equivalent resistance of two 10-Ω resistors, each with a 5% tolerance, placed in parallel? To what percentage tolerance of the equivalent resistance does this range correspond?

5. For a 1-k Ω resistor with tolerance of 2% connected to a 1-volt power supply, what is the range of power that could be dissipated?

PART 1 PROCEDURE 1. Get four resistors with different values of your choosing. Find the nominal values and the tolerances of each resistor using the color codes and record them in Table 1. 2. Set the multimeter to measure resistance, and record the resistance of each resistor in Table 1. 3. Connect each resistor to a 1-volt power supply, one at a time, and measure the voltage across and the current through the resistors. Record the values and determine the resistance using Ohm’s Law in Table 1. 4. Using the resistance as determined in Step 3, calculate the percent deviations from the nominal values and enter them in Table 1. Are the actual values within the tolerances?

9

R1

R2

R3

R4

Color Code Nominal Value Tolerance Ohmmeter reading V/I % deviation from nominal value Actual value within tolerance? Table 1

PART 2 PROCEDURE 1. Construct the circuit in Figure 1 and measure the current that passes through the two resistors. Then simulate in Multisim also. Record this value in Table 2. 2. Measure the voltage across the series combination. Record the value in Table 2. 3. Determine the equivalent resistance of the two series resistors using Ohm’s Law. Record the value in Table 2. Is this value within the combinational tolerance you calculated in the pre-lab? 4. Construct the circuit in Figure 2 and measure the total current that passes through the two resistors. Then simulate in Multisim also. Record this value in Table 3. 5. Measure the voltage across the resistors. Record the value in Table 3. 6. Determine the equivalent resistance of the two parallel resistors using Ohm’s Law. Record the value in Table 3. Is this value within the combinational tolerance you calculated in the pre-lab?

10

Figure 1

Figure 2

I

Hardwire

Multisim

V V/I Actual value within tolerance? Total power dissipated in the two resistors Table 2

I

Hardwire

Multisim

V V/I Actual value within tolerance? Total power dissipated in the two resistors Table 3

11

Experiment 3 Verification of Kirchoff’s Laws INTRODUCTION Kirchoff’s voltage law (KVL) states that the algebraic sum of all voltages around any closed path equals zero. Kirchoff’s current law (KCL) states that the algebraic sum of all the currents at a node is zero (current entering a node has the opposite sign as the current leaving the node). This experiment studies the two laws and acts as verification. OBJECTIVES 1. Practice measuring currents and voltages. 2. Verify Kirchoff’s voltage law. 3. Verify Kirchoff’s current law. MATERIALS DC power supply (1) Multimeter (1) 220-Ω resistor (1) 330-Ω resistor (1) 150-Ω resistor (1) 100-Ω resistor (1) PRE-LAB 1. How many nodes are contained in the circuit in Figure 1? Identify them all by adding an ‘X’ in the figure for each node.

Figure 1

12

2. How many loops are contained in the circuit in Figure 1?

PROCEDURE 1. Construct the circuit shown in Figure 2. Note that nodes C and E are the same node and F and A are the same node; the extra label has only been added for clarity in the following steps. 2. Measure the voltages V_AB, V_BC, V_AD, V_DC, V_BD, and V_AC. Enter the values in Table 1. Note the polarities of the voltages. Repeat in Multisim. 3. Measure the currents I_AB, I_CB, I_AD, I_CD, and I_FA and enter the values in Table 2. Note the polarity (sign) of the currents. Repeat in Multisim. 4. Verify KVL by calculating the sum of the voltages around the following loops and record them in Table 3. ABCEFA ABCDA ADCEFA 5. Verify KCL by adding the currents at nodes A, B, C, D. Enter your results in Table 4.

Figure 2 V_AB

V_BC

V_AD

V_DC

V_BD

V_AC

Multisim Hardwire Table 1 13

I_AB

I_CB

I_AD

I_CD

I_FA

Multisim Hardwire Table 2

ABCEFA

ABCDA

ADCEFA

Sum (Hardwire) Sum (Multisim) Table 3

A

B

C

D

Sum (Hardwire) Sum (Multisim) Table 4

QUESTIONS (these questions all refer to the hardwire circuit, not the Multisim) 1. Were KVL and KCL successfully verified? Give reasons for any discrepancies.

2. KVL is a restatement of one important law of physics. Which law?

3. KCL is a restatement of one important law of physics. Which law? (Your answer will not be the same as for Question 2)

14

Experiment 4 Voltage and Current Dividers for Series and Parallel Circuits INTRODUCTION When two or more resistors are in series, one may derive the voltage across any resistor using KVL and KCL. The end expression is what is known as a voltage divider. Since series combinations of resistors occur often, it is more convenient to memorize the voltage divider expression, rather than deriving it. The same argument can be made for parallel resistors and current dividers. This experiment investigates voltage and current dividers, in particular, when it is appropriate to use them. OBJECTIVES 1. Study the voltage and current relationships of series and parallel circuits. 2. Verify voltage and current dividers and learn when it is appropriate to apply them. MATERIALS DC power supply (1) Multimeter (1) 100-Ω resistor (1) 150-Ω resistor (1) 220-Ω resistor (1) 330-Ω resistor (1) PRE-LAB 1. For the series circuit shown in Figure 1, derive the voltage divider for the voltage V_1 using KVL and noting that the current through R_1 must be the same as the current through R_2 and R_3 (KCL).

2. Using your results from Question 1, write down expressions for V_2 and V_3 (you don’t have to derive them).

3. For the parallel circuit shown in Figure 2, derive the current divider for the current I_1 using KCL and noting that the voltage V_1 must be the same as V_2 (KVL).

15

4. Using your results from Question 3, write down the expression for I_2 (you don’t have to derive it).

5. When are two resistors in series? When are two resistors in parallel?

Figure 1

Figure 2

PROCEDURE 1. Build the circuit in Figure 3 with R_2= 100-Ω, R_3=150-Ω, R_4=220-Ω, and R_6=330-Ω. Let V_s= 5 volts. Take the voltage and current measurements and record them in Table 1. Also measure and record R_eq, the equivalent resistance as seen by the power supply. Repeat in Multisim. 2. Build the circuit in Figure 4 with the same resistor and voltage values. Take the voltage and current measurements and record them in Table 2. Also measure and record R_eq, the equivalent resistance as seen by the power supply. Repeat in Multisim. I_s

I_2

I_3

I_4

I_5

I_6

V_2

V_3

V_4

V_5

V_6

R_eq

Multisim Hardwire

Table 1

16

I_s

I_2

I_3

I_4

I_5

I_6

V_2

V_3

V_4

V_5

V_6

R_eq

Multisim Hardwire

Table 2

Figure 3

17

Figure 4 QUESTIONS (these questions all refer to the hardwire circuit, not the Multisim) Refer to Figure 3 and your results in Table 1 to answer the following questions: 1. Are R_4 and R_6 in parallel, series, or neither? Why? Refer to voltage and current measurements to justify your answer.

2. Are R_3 and R_4 in parallel, series, or neither? Why? Justify.

3. Are V_s and R_3 in parallel, series, or neither? Why? Justify.

4. Are V_s and R_6 in parallel, series, or neither? Why? Justify.

5. Are V_s and R_eq in parallel, series, or neither? Why? Justify.

6. Is voltage division applicable to R_3 and R_4? Why? Justify your answer on the basis of theory given in the pre=lab and introduction.

7. Is current division applicable for R_4 and R_6? Why? Justify your answer on the basis of theory given in the pre=lab and introduction.

8. Is the combination of R_4 and R_6 in series or parallel with R_2? Why? Justify.

18

Refer to Figure 4 and your results in Table 2 to answer the following questions: 9. Are R_4 and R_6 in parallel, series, or neither? Why? Refer to voltage and current measurements to justify your answer.

10. Are R_3 and R_4 in parallel, series, or neither? Why? Justify.

11. Are V_s and R_3 in parallel, series, or neither? Why? Justify.

12. Are V_s and R_6 in parallel, series, or neither? Why? Justify.

13. Are V_s and R_eq in parallel, series, or neither? Why? Justify.

14. Is voltage division applicable to R_3 and R_4? Why? Justify your answer on the basis of theory given in the pre=lab and introduction.

15. Is current division applicable for R_4 and R_6? Why? Justify your answer on the basis of theory given in the pre=lab and introduction.

16. Is the combination of R_4 and R_6 in series or parallel with R_2? Why? Justify.

19

Experiment 5 The Superposition Principle INTRODUCTION One of the most important principles in all of circuit theory states that if there is more than one source in an electric network – be it voltage or course sources – the response can be determined by considering one source at a time. The total response is the algebraic sum of the individual responses. This is known as the superposition principle. While determining the responses with a particular source, all other sources have to be deactivated. OBJECTIVES 1. Verify the superposition principle. MATERIALS DC power supply (2) Multimeter (1) 100-Ω resistor (1) 1-kΩ resistor (1) 220-Ω resistor (1) 330-Ω resistor (1) 1.5-kΩ resistor (1) PRE-LAB 1. Schematic-wise, how do you deactivate a voltage source?

2. Schematic-wise, how do you deactivate a current source?

3. Using superposition, calculate the voltages and currents for each resistor in Figure 1.

20

Figure 1

PROCEDURE 1. Construct the circuit in Figure 1 and measure all the voltages and currents. Record your results in Table 1, and calculate the percent error based on the ideal results from your pre-lab. Repeat for Multisim. 2. Deactivate the 5-volt source from the circuit, and measure the voltages and currents again. Record the results in Table 2. Repeat for Multisim. 3. Put the 5-volt source back into the circuit and deactivate the 10-volt source. Measure all voltages and currents. Record your results in Table 3. Repeat for Multisim. 100-Ω

1-kΩ

220-Ω

330-Ω

1.5-kΩ

Voltage (Multisim) Voltage (Hardwire) % Error voltage (Hardwire) Current (Multisim) Current (Hardwire) % Error current (Hardwire) Table 1

21

100-Ω

1-kΩ

220-Ω

330-Ω

1.5-kΩ

330-Ω

1.5-kΩ

Voltage (Multisim) Voltage (Hardwire) Current (Multisim) Current (Hardwire) Table 2 100-Ω

1-kΩ

220-Ω

Voltage (Multisim) Voltage (Hardwire) Current (Multisim) Current (Hardwire) Table 3

QUESTIONS (these questions all refer to the hardwire circuit, not the Multisim) 1. Check the superposition principle. Enter your observations here.

2. The superposition principle only applies to certain types of circuits. What type?

3. Superposition applies to only some quantities like current and voltage. It does not apply to, for example, power. Why not?

22

Experiment 6 Thevenin’s Theorem and Maximum Power Transfer INTRODUCTION A two terminal resistive network can be replaced by a voltage source in series with an equivalent resistor. The value of the source voltage equals the open circuit voltage of the two terminals under consideration. The value of the equivalent resistor equals the resistance measured between the open terminals when all the sources of the circuit are deactivated. This is Thevenin’s theorem. The voltage source is called the Thevenin voltage (V_TH), and the equivalent resistor, the Thevenin resistance (R_TH). The maximum power that can be output to a variable output resistance occurs when the value of the output resistance equals the Thevenin resistance. OBJECTIVES 1. Learn to construct the Thevenin equivalent circuit. 2. Determine the maximum power condition experimentally. MATERIALS DC power supply (2) Multimeter (1) 10-kΩ resistor (1) 1-kΩ resistor (1) 47-kΩ resistor (1) 33-kΩ resistor (1) Potentiometer (1) PRE-LAB 1. Prove that the maximum power transferred to R_L in Figure 1 occurs when R_L=R_TH.

2. What is the value of the maximum power transferred in terms of V_TH and R_TH?

23

Figure 1 PROCEDURE 1. Construct the circuit given in Figure 2 without the load resistor. 2. Measur the open circuit voltage between points A and B. Record the result in Table 1. This is V_TH for this circuit. 3. With the load resistor still removed, deactivate the two sources. 4. Use a multimeter to measure the resistance between A and B. This is R_TH. Record the result in Table 1. Repeat steps 1-4 for Multisim. 5. Now, you will prove the maximum power condition. Connect the potentiometer R_L between A and B and turn on both voltage sources. 6. Vary R_L between 2.5-kΩ and 10.3-kΩ for a total of about 9 values. For each resistance you choose, measure the voltage between A and B and calculate the power dissipated by R_L. Enter your results in Table 2. 7. Use the supplied graph paper and plot dissipated power (vertical) versus load resistance (horizontal). Label the axes and give your plot a title.

Figure 2

24

V_TH (hardwire)

V_TH (Multisim)

R_TH (hardwire)

R_TH (Multisim)

Table 1

R_L V_L P_L Table 2

25

QUESTIONS (these questions all refer to the hardwire circuit, not the Multisim) 1. According to your graph, for what value of R_L does the maximum transfer of power P_L occur?

2. Does this value of R_L compare with R_TH you obtained experimentally? If not, how much error is there?

3. Draw the Norton equivalent circuit of Figure 1.

4. Suppose you did not know the Thevenin equivalent circuit, what procedure would you follow in the laboratory to get the Norton equivalent circuit?

26

Experiment 7 Measurements of Circuit Transients INTRODUCTION Capacitors are passive components that store charge. It takes time for a capacitor to charge, and this may be good or bad, depending on the application. For something like a filter, where it is desired to treat some frequencies differently than others, the transient response of a capacitor is useful. For applications such as high-speed switching circuits, parasitic capacitances hinder performance. Notice the term “parasitic.” Some capacitances are not from discrete components; rather they are internal to wires, resistors, etc., and cannot be simply removed from the circuit. In this experiment, you will investigate the time it takes to charge a capacitor by simulating the rapid toggling of a switch by a square wave from a function generator. OBJECTIVES 1. Learn how to operate the oscilloscope and function generator. 2. Observe the transient response of a first-order electrical system. 3. Learn how to measure time constants and delays. MATERIALS Oscilloscope (1) Function Generator (1) 3.3-kΩ resistor (1) 33-kΩ resistor (1) 0.1-µF capacitor (1) PRE-LAB 1. The switch in Figures 1 is assumed to be in position “b” long enough for V_0 to reach equilibrium. At some time t=t_0, the switch moves instantaneously to position “a.” Sketch V_0 as a function of time for the time after t_0. What is the time constant?

2. The time constant gives you an idea of how quickly V_0 can change. Obviously the change is too fast for you to operate an actual switch and watch the response. The image would be gone from the oscilloscope screen in a matter of milliseconds. Therefore, you will use the function generator to simulate the repeated flipping of the switch, and the synchronization provided by the scope will form a persistent image by overlapping the repeated output waveforms.

27

The input you need is a periodic voltage waveform that changes repeatedly between zero and five volts; this will replace the voltage source and switch in each circuit. As described in part 1, the source must remain at zero volts and then at 5 volts long enough for V_0 to reach equilibrium. A rule of thumb for the exponential function is that it takes about eight time constants to reach equilibrium. This means you need a square wave of frequency 1/T where T= eight time constants of the RC circuit to be observed. Calculate a suitable frequency for this circuit.

3. Compute the output voltage V_0 when t equals one time constant for the circuit in Figures 1.

4. If the resistor in the figure is changed to 33-kΩ, what is a suitable square wave frequency for observing this circuit? What is the period T of the square wave?

Figure 1

28

PROCEDURE 1. Construct the RC part of the circuit of Figure 1, and replace the switch and voltage source with a signal generator. Using the oscilloscope, adjust the signal generator to produce a square wave with frequency no greater than your calculated value of f. Adjust the amplitude and DC offset so the waveform varies between zero and five volts. 2. Display V_0 on the scope and use part 3 of the pre-lab to measure the time constant. Record the time constant in Table 1. 3. Measure, as well as you can, the rise time t_r of the circuit, defined as the time it takes the output to change from 10% to 90% of its final 5 V value. Record this value here. t_r = 4. Replace the 3.3-kΩ resistor in Figure 1 by a 33-kΩ resistor and repeat step 2. Figure 1, 3.3k

Figure 1, 33k

τ Table 1 QUESTIONS 1. Are your measured time constants from steps 2 and 4 close enough to your prediction to be explained by variation from the nominal values of resistance and capacitance? How do you know?

2. The bandwidth of this circuit is ω_H=1/RC. Compute the bandwidth. Then compare the rise time measured in step 3 with the theoretical value t_r=2.2/ ω_H.

3. Did changing the resistor in steps 5 and 6 change the measured time constants as you expected?

29

APPENDIX ______________________________________________________

30