Steady-State Sinusoidal Behavior Of Linear RLC Circuits

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California State University, Fullerton *

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203L

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Electrical Engineering

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Dec 6, 2023

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pdf

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Andy Nguyen Chuka Okafor Experiment 6 Steady-State Sinusoidal Behavior Of Linear RLC Circuits Group 4
Introduction: In this lab, we will use RLC formulas to test and collect data from circuits with a resistor, an inductor, a capacitor, and a voltage source. Using these formulas we can find Vs, VL, and Vc along with their angles in two different cases—one where the circuit has an open switch and another that is closed. After we used an oscilloscope to find the angles of a voltage source, the voltage of the inductor, and the capacitor. Then, using a voltmeter we found the voltage from the source, the inductor, and the capacitor, both closed and open. After finding the angles and the voltage, we compared the data with the data we found from the formulas. Finally, using a voltmeter we collected data from the circuit using different frequencies. PreLab:
Method: In this lab, we created a circuit using a function generator, an inductor, a capacitor, and a resistor that is kept open from the circuit.
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We set the frequency of the function generator to 5000 Hz and the output to 4.00 volts RMS. After we connected a decade resistance box across the terminals of the generator and adjusted the resistance to find Vs= Vso/2. After we connected the generator to the circuit above and confirmed the voltage predictions made in part II.A.1 and then we closed the circuit and confirmed predictions for part II.B.1. As well as using an oscilloscope we were able to confirm the angles for the two cases. Finally using a voltmeter we varied the frequency of the generator from 100 Hz to 50KHz to find the magnitude of Vc across the range of frequencies. Results: A2) Rs = 50 Ohms, Rs Adjusted= 56 Ohms B) Open Circuit Theoretical Actual Vs 3.638 <6.78 Vs 3.586<7.13 VL 3.63<42.08 VL 3.52<29.63 Vc 2.2<-65.358 Vc 2.14<-73.87 C) Closed Circuit Theoretical Actual Vs 3.16<5.88 Vs 3.12<5.88 VL 3.15<41.18 VL 3.05<27.88 Vc 1.915<-66.51 Vc 1.865<-77.12
D) Magnitude of Vc over a range of Frequencies F (Hz) Vc Theoretical Percent Error 100 2.928 3.198 9.22% 200 2.883 3.192 10.7% 300 2.890 3.181 10.07% 1K 2.866 3.01 5.02% 3K 2.538 2.162 14.8% 5K 2.096 1.524 27% 7K 1.668 1.133 32% 10K 1.168 0.788 32% 20K 0.425 0.332 21% 30K 0.205 0.179 12% 40K 0.117 0.1099 6.06% 50K 0.074 0.0737 0.405%
Conclusion: In this lab, we created an RLC circuit using two resistors, an inductor, a capacitor, and a function generator. By using RLC circuit formulas, we were able to find theoretical values for Vs, VL, and VC as well as their angles. We found these values for two cases, one where the circuit is open and one where it is closed. To verify these predicted values, using a voltmeter we found the actual voltages for Vs, VL, and Vc. While also used an oscilloscope to verify the angle we found for Vs, VL, and Vc for both cases. Finally, using a voltmeter, we found the magnitude of Vc over a range of different frequencies and graphed them and we found that the graph has an exponential decay.
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