Week 3 Lab 1 Capacitors in DC Circuits Lab Report

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Feb 20, 2024

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Carl Electric Circuits Lab Instructor: Cameron Ruddy Capacitors in DC Circuits Student Name(s): Carl Harrison 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: 1/1/2018

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

Abstract The purpose of this lab is to examine how capacitors react in a circuit. We will calculate how capactance values are calculated in series and parallel circuits as well as their RC time constants. Also, we will gain more experience with the Oscilloscope and with the Function generator. I ntroduction The time constant in an RC circuit is a value that states how fast or slow the rate of growth/decay happens when resistors and capacitors are together in a circuit. Capacitors play a crucial role in most DC circuits because of their ability to smooth out current spikes and condition outgoing voltage. Capacitance in a series circuit can be calculated with the following equation: 1 𝐶 𝑒𝑞 = 1 𝐶 1 + 1 𝐶 2 + … + 1 𝐶 𝑛 Capacitance in a parallel circuit can be calculated with the following equation: 𝐶 𝑒𝑞 = 𝐶 1 + 𝐶 2 + … + 𝐶 𝑛 Capacitive reactance is the opposition of current flow through capacitor. It is measured in Ohms and it’s value is inversely related to the frequency of incoming voltage. It is calcuatled with the following equation: 𝑋 𝑐 = 1 2 𝜋 ⋅ 𝐻𝑧 ⋅𝐶 ( 𝐹 ) Procedures Part I: 1. Construct the circuit shown in Figure 1 in Mutism. 3

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Figure 1: Series RC Circuit 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) 4

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. 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 5

7. Calculate the time constant of the RC circuit using the circuit parameter values. Record the result in Table 1 under calculated value.  = 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 VDC ii. Calculate the 63% of the above value 1.84 VDC 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 4.96 VDC  Calculate the 37% of the above value 6.80 VDC  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 ms 212.49 ms 219.70 ms Table 1: Calculated and measured time constant values Calculated Value Measured Value Capacitance .11 µF .11µF Table 2: Series Capacitors Calculated value Measured value using V R Time constant (  ) .110 ms 110 ms Table 3: Calculated and measured time constant values Calculated value Measured value Capacitance .44 µF .439 µF Table 4: Parallel Capacitors 12

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Calculated value Measured value using V R Time constant (  ) .440 ms .435 ms Table 5: Calculated and measured time constant values Calculations Part 1 step 7:  = 1000 Ω * .22 µF = 220 ms Part 2 step 13: C T = (((.22x10^-6)^-1)*2)^-1 = .11 µF Part 2 step 14: C T = (2π * 60 Hz * 24,114Ω) ^-1 = .11 µF Part 2 step 16:  = 1000 Ω * .11 µF = 110 µs Part 2 step 19:  = 4.94 VDC *.37 = 1.84 V Part 3 step 21: C T = .22 µF + .22 µF = .44µF Part 3 step 22: C T = (2π * 60 Hz * 6028.6Ω) ^-1 = .439µF Part 3 step 24:  = .44µF * 1000 Ω = 440ms Required Screenshots Figure 13: Screenshot of Waveforms Part 1 Step 8 13

Figure 14: Screenshot of Waveforms Part 1 Step 11 Figure 15: Screenshot of Impedance Meter Part 2 Step 14 14

Figure 16: Screenshot of Waveforms Part 2 Step 19 Figure 17: Screenshot of Impedance Meter Part 3 Step 22 15

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Figure 18: Screenshot of Waveforms Part 3 Step 27 Conclusion In this lab my calculations matched closely with the values that I observed in the simulation. I was able to prove that multiple capacitors wired in series lowered the overall capacitance of the circuit, while capacitors in parallel increased the overall capacitance. The time constant decreased dramatically when 16

multiple capacitors were wired in series. In parallel, however, the time constant increased commensurate with the increase of capacitance. Capacitive Reactance is directly proportional with capacitance, so 𝑋 𝐶 increased in a parallel circuit and decreased in a series circuit. 17

References Floyd, T. L., & Buchla, D. M. (2019). Principles of Electric Circuits (10th Edition). Pearson Education (US). https://bookshelf.vitalsource.com/books/9780134880068 Last Name, First initial. Second initial (Date of Video). Title and Subtitle of Video . Video URL Capacitors in series and parallel . Capacitors in Series and Parallel - Capacitors - Basics Electronics. (2021, June). https://ecstudiosystems.com/discover/textbooks/basic- electronics/capacitors/capacitors-in-series-and-parallel/ 18

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