California State University, Fullerton Department of Electrical and Computer Engineering EGEC 203L-08 Electric Circuits Laboratory Assignment 8 RLC Circuit: Impedance Measurement Submit only copy per team Before submitting, verify that your submitted files are readable • • Read all parts before your start Part A Spring 2024 RLC circuits and preparation Make yourself familiar with RLC circuits. Read the relevant sections in the lab manual and the circuits textbook. Review background information on capacitive reactance, inductive reactance, resistance, and impedance. Review phasor diagrams. Complete Part I of Experiment 7 in the Lab Manual (Page 61) Complete Part II ((A, B and C) of Experiment 7 in the Lab Manual (Page 61-62) (Lab) Complete parts A and B in the manual (pages 62 and 63). Part B • Turn in a completed and filled copy of this handout on Canvas showing all relevant calculations, data and results (in PDF format). All of these must be included in the report as well, in the relevant sections. Do not omit any details in the report. • Also turn in an informal report via Canvas in PDF format. Your report shall include: 1. Title page. This page must include the title of the assignment, the full names of the team members and date of report completion 2. Introduction 3. Theoretical background. Use information from multiple sources, at least two. List those sources in the report. 4. Tools and Equipment 5. Procedure 6. Observations, Calculations, Measurements and Results 7. Discussion 8. Conclusions CALIFORNIA STATE UNIVERSITY, FULLERTON ELECTRICAL ENGINEERING EG-EE 203L Experiment 7 VOLTMETER MEASUREMENT OF AN UNKNOWN IMPEDANCE I. BACKGROUND The purpose of this experiment is to show how the value of an impedance can be determined with a minimum of instrumentation. At the same time a study is made of the behavior of a particular simple circuit. The circuit to be used for determining an unknown impedance, Z, is as shown in Fig. 1. The magnitudes of Vs, VR and Vz can be measured with the Digital Voltmeter. Vs + VR - w R Zt +1 Vz FIG. 1 Knowing R, the magnitude of Z can now be calculated. By means of a graphical construction of the related phasor diagram, or of the equivalent trigonometrical calculation, the magnitude of the phase angle can be found. The sign of the phase angle can be determined from the knowledge that an inductive impedance will increase if the frequency is increased slightly, whereas a capacitive impedance will decrease if the frequency is increased slightly. The three things thus found completely determine Z. II. PREPARATION A. Sketch a typical phasor diagram showing the relationship between Vs, VR and Vz for each of the following cases. Place Vs in the horizontal position pointing to the right. 61 1. Z is equivalent to the series combination of an inductance and a resistance. 2. Z is equivalent to the series combination of a capacitance and a resistance. B. Calculate literally (with letters, not numbers) the value of Z in terms of R and the voltages. C. Show how to determine the magnitude of the phase angle of Z from the phasor diagram: 1. Show the phase angle in the phasor diagrams sketched in Part II.A. 2. Calculate the magnitude of the phase angle trigonometrically in terms of the voltages. III. IN THE LABORATORY For each individual measurement made, connect the unknown impedance in a circuit as shown in Fig. 1, set the frequency of Vs using the frequency counter, set Vs approximately to 5 volts, and adjust R so that Vz is approximately equal to VR in magnitude. Do not waste time trying to be exact with the voltage settings. Then record R and make good measurements of Vs, VR and Vz with the digital voltmeter. Finally, test to see whether Z is inductive or capacitive. A. Use the series combination of a 200 ohm resistor and a 10 mH inductor as the unknown impedance Zt. XL = WL 1. Make the above measurements at a frequency of 7000 Hz. 2. Calculate Zt. 217500 Vs 3. Draw a large phasor diagram carefully to scale based on your data. Measure the phase angle of Zt. 4. Calculate the phase angle of Zt trigonometrically. Compare the value obtained graphically with the calculated value. B. Construct the circuit shown in Fig. 2 using the same elements for Zt as in part III.A. Consider that the circuit between the two left-hand terminals is one equivalent unknown impedance, Ze. 62 CALIFOR DEPARTM 500 Ω Ze- 0.05 µF Zt FIG. 2 C 1. Using the value of Zt determined in parts III.A.2 and III.A.4, calculate the value of Ze at 7000 Hz. Ze=700 2. Determine Ze experimentally. Compare with the calculated value. Z=610