Week 2 Lab 2 Series RL Circuits Lab Report (1)

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Feb 20, 2024

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Electric Circuits Lab Instructor: ----------- Series RL Circuits Student Name(s): Carl Harrison Click or tap here to enter text. Honor Pledge: I pledge to support the Honor System of ECPI. I will refrain from any form of academic dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the academic community, it is my responsibility to turn in all suspected violators of the honor code. I understand that any failure on my part to support the Honor System will be turned over to a Judicial Review Board for determination. I will report to the Judicial Review Board hearing if summoned. Date: 1/1/2018

Contents Abstract ....................................................................................................................................................... 3 I ntroduction ................................................................................................................................................ 3 Procedures .................................................................................................................................................. 3 Data Presentation & Analysis ...................................................................................................................... 4 Calculations ............................................................................................................................................. 4 Required Screenshots .............................................................................................................................. 4 Conclusion ................................................................................................................................................... 4 References ................................................................................................................................................... 5 2

Lab Report Instructions: (This instruction box is to be deleted before submission of the Lab report) Before starting on your lab report, please follow the following steps: 1) Follow the instructions listed provided in the lab instructions. 2) Complete this lab report . Upon completion, you will submit this lab report and your working Multisim files to your instructor. Abstract (This instruction box is to be deleted before submission of the Lab report) What is an Abstract? This should include a brief description of all parts of the lab. The abstract should be complete in itself. It should summarize the entire lab; what you did, why you did it, the results, and your conclusion. Think of it as a summary to include all work done. It needs to be succinct yet detailed enough for a person to know what this report deals with in its entirety. Objectives of Week 2 Lab 2:  Understand the effect of frequency on inductive reactance.  Measure the impedance of an RL circuit.  Measure the phase angle and phase lead of an RL circuit using the oscilloscope.  Draw the impedance and voltage phasor diagrams.  Understand how an inductor differentiates current. I ntroduction (This instruction box is to be deleted before submission of the Lab report) What is an Introduction? In your own words, explain the reason for performing the experiment and give a concise summary of the theory involved, including any mathematical detail relevant to later discussion in the report. State the objectives of the lab as well as the overall background of the relevant topic. Address the following items in your introduction:  What is Impedance for an RL circuit? (Give formula)  What is phase angle for an RL circuit? How is it calculated?  What is phase lead for an RL lead circuit? How is it calculated?  How/why does an inductor differentiate current? Give formula. 3

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Procedures (This instruction box is to be deleted before submission of the Lab report) This section should contain the procedures as outlined in the lab instructions. Part I : 1. Connect the following circuit. R 1kΩ L 100mH 1Vrms 1 kHz Figure 1: RL Circuit 2. Connect one DMM across the resistor and one DMM across the inductor. Set both DMMs to read AC Voltage. Measure the voltage drop across each component. Record the result in Table 1 . 3. Use Ohm’s law to calculate the current flowing through the resistor. Since the circuit in Figure 1 is a series RL circuit, the same current will flow through the inductor and the resistor. Record the result in Table 1 . Total current I = V R R 4. Calculate the inductive reactance using Ohm’s law. Record the result in Table 1 . Inductive Reactance X L = V L I 5. Finally, calculate the inductive reactance using the inductive reactance equation. Record the result in Table 1 . Inductive Reactance , X L = 2 πfL 4

6. Adjust the function generator frequency following the steps in Table 2 . Use the DMM to measure the voltage across the resistor and the inductor. Record your measurements in Table 2 . 7. Plot the graph for Frequency vs. V L . Part II: 8. Build the circuit in Figure 2 . Figure 2: Series LR Circuit 9. Set the voltage source amplitude to 1.5 V P and frequency to 25 kHz, sine wave 10. Connect Channel A of the oscilloscope across the resistor and measure the peak voltage drop (V R ). Record the result in Table 3 . 11. Use Ohm’s law to calculate the peak current flowing through the resistor. Because it is a series circuit, the same current will flow through the inductor. Record the result in Table 3 . Total current I = V R R 12. Connect Channel B of the oscilloscope across the inductor and measure the peak voltage drop (V L ). Record the value in Table 3 . 13. Calculate the inductive reactance using Ohm’s law. Record the result in Table 3 . Inductive Reactance X L = V L I 5

14. Now, calculate the total impedance (Z T ) value using the equation . Record the result in Table 3 . Total Impedance (Z T ) = V S I 15. Calculate the phase angle between V R and V S using the formula . Record the result in Table 3 above. Also, record this value in Table 4 under Phase Angle calculated value. Phase angle, θ = tan − 1 ( X L R ) Part III: Phase Angle and Phase Lead Measurement Phase Angle 16. Connect Channel B of the oscilloscope across the voltage source and run the simulation. Channel A should still be connected across the resistor. 17. The waveforms should look like the ones shown in Figure 4 . Figure 4: V S and V R waveforms 18. Obtain a stable display showing a couple of cycles for Channel B (which is showing V S ) and disable Channel A by setting it to 0. 6

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19. Measure the time period (T) of the source voltage. Record the result in Table 4 . (Use the cursors to measure the period (on the scope it will show as T2-T1). Remember that the period is the time taken to complete one cycle). See Figure 5 . Figure 5: Measuring time period (T) 20. Now set the oscilloscope to view both the channels. 21. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both channels appear to have same amplitude as seen on the scope face. (as close as possible) 22. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are just visible across the screen as shown . 23. Measure the time duration between the two signals (∆t) and record the result in Table 4 . (Use cursors as shown in Figure 6 ) 7

Figure 6: Measuring the time difference 24. Calculate the phase angle using the formula and record the result in Table 4 . Phase angle, θ = (∆t/T) * 360° Phase Lead 25. Connect your circuit as shown in Figure 7 . When the output of an RL circuit is taken across the inductor, the circuit is called an RL lead circuit. The output voltage in an RL lead circuit will lead the input voltage. Figure 7: RL Lead Circuit 8

26. Calculate the phase lead using the equation . Notice the similarity to the equation for the phase angle. The phase lead angle and phase angle of an RL circuit are complementary angles. (Their sum is 90°.) Use R and X L values from Table 3. Phase Lead, ϕ = tan − 1 ( R X L ) 27. Measure the time period (T) of the source voltage (as in Step 19). Record this value in Table 4 . 28. Now set the oscilloscope to view both the channels. 29. Adjust the amplitude of the signals using Channel A and Channel B V/Div scale until both channels appear to have the same amplitude as seen on the scope face. (as close as possible) 30. Spread the signals horizontally using the Timebase (Sec/Div) control until both signals are just visible across the screen as shown in Figure 6 . 31. Measure the time duration between the two signals (∆t) and record the result in Table 4 . 32. Calculate the phase lead using the formula and record the result in Table 4 . Phase lead, θ = (∆t/T) * 360° 33. Plot the Voltage and Impedance Phasor Diagrams. Clearly indicate the phase angle and the phase lead. Part IV: The Inductor Differentiates Current 34. Construct the following RL circuit in Multisim. Set the triangular current source to 1mA and 1ms. 9

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Figure 8: Differentiator Circuit 35. Connect Channel A across the resistor and Channel B across the inductor. (Note: change one or both trace colors to better observe the two signals) 36. Your signals should look like the example in Figure 9 . Figure 9: Inductor as a differentiator waveforms 37. Channel A will show the voltage across the resistor. This signal can be used to find the circuit current using Ohm’s law. 38. Channel B shows the voltage across the inductor. Show that this signal satisfies the following equation on the piecewise differentiable intervals. 10

v L ( t ) = L di dt 39. Refer to Figure 10 to answer the following questions. Figure 10: Differentiator values, 0 to 0.5 ms a. The signal has a period of 1 ms. Write the equation for the circuit current on the interval 0 to 0.5 ms by following the steps. i ( t ) = v R ( t ) R b. The general equation of a line is y = mx + b . 11

We will start by finding v R (t). In this case, y is v R (t) and m is the slope of the voltage. Fill in the values of v R (0.5) and v R (0) to find the slope. Channel A, Cursor T2 gives the resistor voltage at t=0. Channel A, cursor T1 gives the resistor voltage at t = 0.5 ms. m = Δv Δt = v R ( .5 ) − v R ( 0 ) 0.5 ms − 0 ms c. Next, find b, the voltage at the beginning of the interval, v(0), expressed in volts. d. Write the equation for the resistor voltage on the interval of 0 to 0.5 ms using the values above. v ( t ) = mt + v ( 0 ) e. Find the equation for i(t) i ( t ) = v R ( t ) R f. Find the equation of v L (t) by differentiating i(t). g. Compare this value to the v L (t) waveform. 40. Refer to Figure 11 to answer the following questions. 12

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Figure 11: Differentiator values, 0.5 ms to 1.0ms a. The signal has a period of 1 ms. Write the equation for the circuit current on the interval 0.5 ms to 1.0 ms by following the steps . i ( t ) = v R ( t ) R b. The general equation of a line is y = mx + b . We will start by finding v R (t). In this case, y is v R (t) and m is the slope of the voltage. Fill in the values of v R (0.5) and v R (1.0) to find the slope. Channel A, Cursor T2 gives the resistor voltage at t = 50 ms. Channel A, cursor T1 gives the resistor voltage at t = 100 ms. 13

m = Δv Δt = v R ( 1.0 ) − v R ( 0.5 ) 1.0 ms − 0.5 ms c. Next, find b, the voltage at the beginning of the interval, v(0.5), in volts d. Write the equation for the resistor voltage on the interval of 0.5 ms to 1.0 ms using the values v ( t ) = mt + v ( 0.5 ) e. Find the equation for i(t) i ( t ) = v R ( t ) R f. Find the equation of v L (t) by differentiating i(t). g. Compare this value to the v L (t) waveform. Data Presentation & Analysis Table 1: Calculated and measured values 14 Inductor L 1 Voltage across, R .846 V Voltage across, L .533 V Total Current, I .846 mA Inductive Reactance, X L 630.02Ω Computed Reactance, X L 628.32 Ω

Table 2: Calculated and measured values Table 3: Calculated and measured values 15 Frequency (in Hz) V R (measured) V L (measured) I = V R R X L = V L I X L = 2πfL (calculated) 300 0.983 V 0.186 V .983 mA 189.22 Ω 188.50 Ω 1k 0.846 V 0.533 V .846 mA 630.02 Ω 628.32 Ω 3k 0.467 V 0.884 V .467 mA 1892.93 Ω 1885 k Ω 5k 0.303 V 0.953 V .303 mA 3145.21 Ω 3141k Ω 7k 0.221 V 0.975 V .221 mA 4411.76 Ω 4398k Ω 9k 0.174 V 0.985 V .174 mA 5660.92 Ω 5654k Ω 11k 0.143 V 0.99 V .143 mA 6923.08 6912k Ω 13k 0.121 V 0.993 V .121 mA 8206.61 Ω 8168k Ω 15k 0.105 V 0.994 V .105 mA 9466.67 Ω 9425k Ω V R I V L X L Z T θ

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(Use Word or Excel to create the plot and place here.) Plot 1: Frequency vs. Inductor Voltage Type of Angle Measured Period (T) Time difference (∆t) Measured Angle Calculated Angle Phase angle θ Phase Lead Φ Table 4: Phase angle and phase lead measurements (Use Word or Excel to create the Phasor Diagrams and place here.) Plot 2(a) Impedance Phasor Plot 2(b) Voltage Phasor Calculations Part I step 3: I = 16

Part I step 4: X L = Part I step 5: L = Part II step 11: I = Part II step 13: X L = Part II step 14: Z T = Part II step 15: θ = ¿ Part III step 24: ∅ = ¿ Part III step 26: ∅ = ¿ Part III step 32: θ = ¿ Part IV step 39 b: m = ( 𝑦 2 − 𝑦 1 ) ( 𝑥 2 − 𝑥 1 ) = ( − 97.85 𝑚𝑉 − 49.68 𝑚𝑉 ) .5 𝑚𝑠 = ¿ -295.06 Part IV step 39 d: v R (t) = -295.06t -48.165mV Part IV step 39 e: i(t) = Part IV step 39 f: v L (t) = Part IV step 41 b: m = Part IV step 41 d: v R (t) = Part IV step 41 e: i(t) = Part IV step 41 f: v L (t) = Required Screenshots Figure 12: Screenshot of Waveforms Part 3 Step 10 17

Figure 13: Screenshot of Waveforms Part 3 Step 12 Figure 14: Screenshot of Waveforms Part 3 Step 19 18

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Figure 15: Screenshot of Waveforms Part 3 Step 23 Figure 15: Screenshot of Waveforms Part 3 Step 27 19

Figure 16: Screenshot of Waveforms Part 3 Step 31 20

Conclusion (This instruction box is to be deleted before submission of the Lab report) What is a Conclusion? This section should reflect your understanding of the experiment conducted. Important points to include are a brief discussion of your results, and an interpretation of the actual experimental results as they apply to the objectives of the experiment set out in the introduction should be given. Also, discuss any problems encountered and how they were resolved. Address the following in your conclusions:  Were your measured and calculated inductive reactance values in agreement?  What happened to the inductance and the inductive reactance as you increased the frequency of the voltage source?  Were your measured and calculated phase angle values in agreement?  Which quantity leads in a series RL circuit? (Current or voltage) How do you know?  What happens to phase angle as the frequency increases? What happens to phase angle as the frequency decreases?  Were your measured and calculated phase lead values in agreement?  Which quantity leads in an RL lead circuit? (Source voltage or inductor voltage)  What is the relationship between phase angle and phase lead?  What happens to the phase lead as the frequency increases? What happens to the phase lead as the frequency decreases? 21

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References (This instruction box is to be deleted before submission of the Lab report) What is a Reference Section? This section should list all sources used in the completion of the lab report using APA format. At a minimum, you should include your book and your instructor’s notes and videos. Be sure to list all sources to avoid plagiarism. Note: The reference section contains the reference for your book. Add to it as necessary. The second entry is the way to cite your instructor’s Zoom video. Floyd, T. L., & Buchla, D. M. (2019). Principles of Electric Circuits (10th Edition). Pearson Education (US). https://bookshelf.vitalsource.com/books/9780134880068 Last Name, First initial. Second initial (Date of Video). Title and Subtitle of Video . Video URL 22

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