5CL Lab 6 Submission Template - S23

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University of California, Los Angeles *

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Electrical Engineering

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Feb 20, 2024

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Activity 1 - Measuring Resistance and Capacitance: List your 12 resistor-capacitor combinations with their measured (not printed) values. Calculate the predicted RC time constants for each of these 12 combinations with the measured values. Show your results in data table format.

Activity 2 - Simple RC Circuit: Draw the circuit diagram for your simple RC circuit. Include the PASCO voltmeter and label the battery voltage, the resistance of your resistor, and the capacitance of your capacitor (measured values). Include your voltage vs. time plot(s) that show your data for both charging and discharging. Report your fit values (A, B, t 0 for rise, A, B, y 0 for discharge). Resistance→100K ohm, measured 98900 ohm Capacitance→10μf, measured 0.00001177 f Voltage=6V Rise: A = 5.34 +- 6.2 x 10^-4 B = 0.931 +- 0.0011 t 0 = 4.48 +- 8.82 x 10^-4 Discharge: A = 24 +- 0.075 B = 0.0836 +- 1.6 x 10^-4 y 0 = 0.0789 +- 0.0026

Activity 2 - Simple RC Circuit (cont.): How does the rise A parameter compare with your power supply voltage? What is your measured RC time constant for the voltage rise and how does it compare to your prediction? Using the decay RC time constant and your measured capacitance, what is the resistance in the PASCO voltmeter? Our Rise A parameter is A = 5.34 +- 6.2 x 10^-4 and our power supply voltage is 6V. Therefore, our Rise A parameter is smaller than the power supply voltage. RC time constant is t = 1/B → B = 1.074 s, which was just slightly below our predicted value. t = RC → R = t/C = 1.19 kΩ

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Activity 3 - Capacitors in Series: Draw the circuit diagram for your capacitors in series and label the resistance of your resistor, the capacitance of your capacitors, and the voltage on your power supply. What is the equivalent capacitance of the two capacitors? Does the capacitance increase or decrease when capacitors are in series? What do you predict your RC time constant will be? Sketch the voltage vs time plot (rise only, no discharge). Report your best fit parameters (A, B, t 0 ). How does the rise A parameter compare with your power supply voltage. What is your measured RC time constant for the voltage rise and how does it compare to your prediction? C eq = (1/100 + 1/470)^-1 = 82.46 uF = 0.0000824 F The capacitance decreases when capacitors are in series A = 5.46 +- 1.8 x 10^-4 B = 0.115 +-2.1 x 10^-5 t 0 = 2.78 +- 8.6 x 10^-4 Predicted RC = (98900ohm)(0.0000824F) = 8.15 sec The rise A parameter is a little bit less than the power supply voltage. The measured RC time constant is 1/B = 1/0.115 = 8.7 sec, which is around the predicted RC of 8.15

Activity 4 - Capacitors in Parallel: Draw the circuit diagram for your capacitors in parallel and label the resistance of your resistor, the capacitance of your capacitors, and the voltage on your power supply. What is the equivalent capacitance of the two capacitors? Does the capacitance increase or decrease when capacitors are in parallel? What do you predict your RC time constant will be? Sketch the voltage vs time plot (rise only, no discharge). Report your best fit parameters (A, B, t 0 ). How does the rise A parameter compare with your power supply voltage. What is your measured RC time constant for the voltage rise and how does it compare to your prediction? C eq = 10 + 100 = 110 uF The capacitance increase when capacitors are in parallel. Predicted RC = (98900ohm)(0.00011F) = 10.879 sec A = 5.43 +- 1.3 x 10^-4 B = 0.0857 +- 9.1 x 10^-6 t 0 = 7.554 +- 5.8 x 10^-4 The rise A parameter is a little bit less than the power supply voltage. The measured RC time constant is 1/B = 1/0.0857 = 11.67 sec, which is a little higher than the predicted RC of 10.879