Series RL Circuits: Phase Angle, Phase Lead, and Inductors as Differentiators

I. Objectives:

After completing this lab experiment, you should be able to:

1. Understand the effect of frequency on inductive reactance.

2. Measure the impedance of an RL circuit.

3. Measure the phase angle and phase lead of an RL circuit using the oscilloscope.

4. Draw the impedance and voltage phasor diagrams.

5. Understand how an inductor differentiates current.

II. Parts List:

1. Resistors 100 Ω, 1 kΩ, 10 kΩ.

2. Inductors 1 µH, 100mH.

III. Procedures:

Part I :

1. Connect the following circuit.

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 =

4. Calculate the inductive reactance using Ohm’s law. Record the result in Table 1.

Inductive Reactance XL =

5. Finally, calculate the inductive reactance using the inductive reactance equation. Record the result in Table 1.

Inductor L1

Voltage across, R

845.958 mV

Voltage across, L

533.246 mV

Total Current, I

0.846 mA

Inductive Reactance, XL

630.35 ohms

Computed Reactance, XL

628.32 omhs

Table 1: Calculated and measured values

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.

Frequency (in Hz)

VR

(measured)

VL

(measured)

I =

XL =

XL = 2πfL

(calculated)

300

982.58 mV

185.81 mV

0.9856 mA

189.10 ohms

188.50 ohms

1k

845.958 mV

533.246 mV

0.846 mA

630.35 ohms

628.32 ohms

3k

467.467 mV

833.996 mV

0.468 mA

1.78 kΩ

1.88kΩ

5k

302.425 mV

953.161 mV

0.302 mA

3.15 kΩ

3.14 kΩ

7k

221.027 mV

975.265 mV

0.221 mA

4.41 kΩ

4.40 kΩ

9k

173.593 mV

984.811 mV

0.174 mA

5.66 kΩ

5.66 kΩ

11k

142.743 mV

989.751 mV

0.143 mA

6.92 kΩ

6.91 kΩ

13k

121.133 mV

992.626 mV

0.121 mA

8.20 kΩ

8.17 kΩ

15k

105.174 mV

994.442 mV

0.105 mA

9.47 kΩ

9.43 kΩ

Table 2: Calculated and measured values

7. Plot the graph for Frequency vs. VL.

(Use Word or Excel to create the plot)

Figure 2. Plot of Frequency vs. Inductor Voltage

Part II:

8. Build the circuit in Figure 2.

Diagram, schematic Description automatically generated

Figure 2: Series LR Circuit

9. Set the voltage source amplitude to 1.5 VP and frequency to 25 kHz, sine wave

10. Connect Channel A of the oscilloscope across the resistor and measure the peak voltage drop (VR). 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 =

VR

I

VL

XL

ZT

1.133 V

0.113 mA

1.786 V

15.80 kΩ

13.27 kΩ

46.49ᶿ

Table 3: Calculated and measured values

12. Connect Channel B of the oscilloscope across the inductor and measure the peak voltage drop (VL). Record the value in Table 3 above.

13. Calculate the inductive reactance using Ohm’s law. Record the result in Table 3.

Inductive Reactance XL =

14. Now, calculate the total impedance (ZT) value using the equation. Record the result in Table 3.

Total Impedance (ZT) =

15. Calculate the phase angle between VR and VS using the formula. Record the result in Table 3. Also, record this value in Table 4 under Phase Angle calculated value.

Phase angle,

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.

Histogram Description automatically generated with medium confidence

Figure 4: VS and VR waveforms

18. Obtain a stable display showing a couple of cycles for Channel B (which is showing VS) and disable Channel A by setting it to 0.

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.

Diagram Description automatically generated

Figure 5: Measuring time period (T)

Graphical user interface Description automatically generated

Type of Angle

Measured

Period (T)

Time difference (∆t)

Measured Angle

Calculated Angle

Phase angle θ

40 ms

6.4 ms

57.6

57.6

Phase Lead Φ

Table 4: Phase angle and phase lead measurements

Graphical user interface Description automatically generated

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 the 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)

Diagram Description automatically generated

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.

Diagram, schematic Description automatically generated

Figure 7: RL Lead Circuit

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 XL values from Table 3.

Phase Lead,

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.