Week 3 Lab 1 Capacitors in DC Circuits Lab Report

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Dec 6, 2023

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Electric Circuits Lab Instructor: Cameron Ruddy Capacitors in DC Circuits Student Name(s): Brandon Walker 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: 0/18/2023

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

Abstract We will be learning in this lab how to measure resistance of capacitors and capacitance of RC circuits. We will be using function generators and an oscilloscope to help with our measurements. We will learn the effects of series and parallel in RC circuits time constants with the use of Vr, and Vc. I ntroduction We will be performing experiments to help us learn what the time constant for a RC circuit is and why this is important. We find that time constant is t=RxC and this determines the rate of charging and discharging in the circuit. Capacitors in series combine with the formula 1/ctotal=1/c1+1/c2+1/c3 for how every many capacitors in series. When capacitors are connected in parallel we use the equation Ctotal=C1+C2… for how every many capacitors in parallel. Capacitive reactance is how much capacitors resist the flow of AC with the formula XC=1/2piefC Procedures Part I: 1. Construct the circuit shown in Figure 1 in Mutism. Figure 1: Series RC Circuit 3

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2. Connect Channel A of the oscilloscope across the voltage source and Channel B across the capacitor. 3. Set the function generator to 5V pp ; 100 Hz, Square Wave 50% duty cycle with 2.5 DC offset if using a function generator . If using clock voltage, set it to 5V pp , 100 Hz. The DC offset can be modeled by using DC mode on the oscilloscope. 4. Observe the signals on the scope screen. See Figure 2(a) below. (Use Volts/Div and Time/DIV settings to adjust the signal) Figure 2(a): Voltage across the Voltage Source and the capacitor 5. Disable Channel A, by setting it to 0, while observing Channel B. You should be able to see the waveform as shown below. Use time base and Channel A scale to adjust the signal. 4

Figure 2(b): Voltage across the capacitor 6. Change the time base (Sec/Div) until you have a clear waveform on the scope as shown in Figure 2(c). Figure 2(c): Voltage across the capacitor 7. Calculate the time constant of the RC circuit using the circuit parameter values. Record the result in Table 1 under calculated value. 5

 = R*C 8. Measuring the time constant with V C : i. Measure the peak value of the signal, by placing one of the cursors (T1) at the peak point ___5.00v______. ii. Calculate the 63% of the above value ___3.15v______. iii. Place the second cursor (T2) at the step (ii) value above and T1 at zero just before the capacitor voltage starts rising as shown in Figure 3 . iv. Observe the value of T2-T1 on the scope, which is the one time constant, as shown below. v. Record the result in Table 1 above under measured value using V C . Figure 5: Measuring RC time constant using V C 9. Connect Channel B of the oscilloscope across the resistor. 10. You should be able to see the waveform as shown below. (Use Volts/Div and Time/DIV knobs to adjust the signal) 6

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Figure 6(a): Voltage across the resistor 11. Measuring the time constant with V R :  Measure the peak value of the signal, by placing one of the cursors (T1) at the peak point ______5.00v___.  Calculate the 37% of the above value ____1.85_____.  Place the second cursor (T2) at the step (ii) value above.  Observe the T2-T1 value on the scope, which is the one time constant.  Record the result in Table 1 above under measured value using V R . 7

Figure 6(b): Measuring RC time-constant using V R Part II: 12. Place two capacitors in series as shown in Figure 7 below. Figure 7: Series Capacitors 13. Calculate the total capacitance value and record the results in Table 2 . C T = 1 1 C 1 + 1 C 2 14. Measure the total capacitance value. Use the following procedure to measure the capacitance in Multisim.  Connect the impedance Meter (Simulate>>Instruments>>LabView Instruments>>Impedance Meter) as shown in Figure 8 .  Measure the capacitive reactance, X C , as shown in Figure 8 .  Calculate the capacitance using the equation, C = 1 2 πf X C and record the value in Table 2 . Figure 8: Impedance Meter in Multisim 8

15. Modify the circuit as shown below, by placing two 0.22µF capacitors in series as in Figure 8 . Figure 8: RC circuit with two series capacitors 16. Calculate the new RC time constant using measured values. Record the result in Table 3. 17. Connect Channel A of the oscilloscope across the resistor 18. Adjust the trigger if needed, and you should be able to see the waveform as shown in Figure 9 below. Figure 9: Voltage Across the Resistor 19. Repeat step 11. Record the measured time constant in Table 3 . 9

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Part III: 20. Place two capacitors in parallel as shown in Figure 10 below. ( Note: The 0.001 Ω resistor is ONLY required for simulation in Multisim. Without the resistor, the mathematical model will not converge). Figure 10: Parallel Capacitors 21. Calculate the total capacitance value and record the results in Table 4 below. C T = C 1 + C 2 22. Measure the total capacitance value. Use the following procedure to measure the capacitance in Multisim.  Connect the impedance Meter (Simulate>>Instruments>>LabView Instruments>>Impedance Meter).  Measure the capacitive reactance.  Calculate the capacitance using the equation, C = 1 2 πf X C and record the value in Table 4. 23. Modify the circuit by placing two 0.22µF capacitors in parallel as in Figure 11. 10

Figure 11: RC Circuit with Parallel Capacitors 24. Calculate the new RC time constant using measured values. Record the result in Table 5 . 25. Connect Channel A of the oscilloscope across the resistor. 26. You should be able to see the waveform as in Figure 12 below. (Use Volts/Div and Time/DIV knobs to adjust the signal) 27. Use the cursors on the oscilloscope to measure the time constant (refer to step 11). Record the result in Table 5 under measured value. Figure 12: Voltage across the resistor 11

Data Presentation & Analysis Calculated value Measured value using V C Measured value using V R Time constant (  ) 220.000uS 274.621uS 220.251uS Table 1: Calculated and measured time constant values Calculated Value Measured Value Capacitance 0.11uF 0.11uF Table 2: Series Capacitors Calculated value Measured value using V R Time constant (  ) 110.000uS 109.848 Table 3: Calculated and measured time constant values Calculated value Measured value Capacitance 0.44uF 0.44uF Table 4: Parallel Capacitors Calculated value Measured value using V R Time constant (  ) 440.000uS 457.880 Table 5: Calculated and measured time constant values 12

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Calculations Part 1 step 7:  = 220.000uS Part 2 step 13: C T =0.11uF Part 2 step 14: C T =0.11uF Part 2 step 16:  = 110.000uS Part 2 step 19:  = 109.848 Part 3 step 21: C T =0.44uF Part 3 step 22: C T =0.44uF Part 3 step 24:  = 440.000uS Required Screenshots Figure 13: Screenshot of Waveforms Part 1 Step 8 Figure 14: Screenshot of Waveforms Part 1 Step 11 13

Figure 15: Screenshot of Impedance Meter Part 2 Step 14 Figure 16: Screenshot of Waveforms Part 2 Step 19 14

Figure 17: Screenshot of Impedance Meter Part 3 Step 22 Figure 18: Screenshot of Waveforms Part 3 Step 27 15

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Conclusion  Did your measured results match your calculated values? If not, why not? Yes my values did match very close to the calculated values.  What happened to the overall capacitance when you went from one series capacitor to two? (Did capacitance increase or decrease?) When capacitors are added in series the overall capacitance decreases.  What happened to the overall capacitive reactance when you went from one series capacitor to two? (Did the capacitive reactance increase or decrease?) The capacitive reactance increases when capacitors are added in series.  What happened to the time constant when you went from one series capacitor to two? (Did the time constant increase or decrease?) The time constant decreased since the overall capacitance decreased.  What happened to the overall capacitance when you went from one capacitor to two parallel capacitors? (Did the capacitance increase or decrease?) The capacitance increased when going from one to two parallel capacitors.  What happened to the overall capacitive reactance when you went from one capacitor to two parallel capacitors? (Did the capacitive reactance increase or decrease?) The capacitance reactance decreases going from one to two parallel capacitors.  What happened to the time constant when you went from one capacitor to two parallel capacitors? (Did the time constant increase or decrease?) The time constant increases going from one to two parallel capacitors. 16

References Floyd, T. L., & Buchla, D. M. (2019). Principles of Electric Circuits (10th Edition). Pearson Education (US). https://bookshelf.vitalsource.com/books/9780134880068 17