2101 Lab 2 Capacitors and Inductors

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ECE 2101L Section 8 Electrical Circuit Analysis II Lab LAB 2 Capacitors and Inductors with DC Sources Review 09/06/2023

ABSTRACT This report observes circuit analysis in the steady state cases of RC and RL circuits. Both cases behave inversely with one another as we learn that inductors may be treated as a short circuit and capacitors can be treated as open circuits. 2

Table of Contents Page Abstract…………………………………………………………………………2 List of Figures…………………………………………………………………..5 List of Tables……………………………………………………………………4 I. Objectives………………………………………………………………...6 II. Pre-Lab…………………………………………………………………...6 III. Lab………………………………………………………………………..7 IV. Conclusion……………………………………………………………….14 V. Post Lab………………………………………………………………….15 3

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LIST OF TABLES Table 1.1……………………………………………...7 Table 1.2……………………………………………...8 Table 1.3……………………………………………..10 Table 1.4……………………………………………..10 Table 1.5……………………………………………..12 Table 1.6……………………………………………..12 Table 1.7……………………………………………..12 4

LIST OF FIGURES Figure 1.1………………………………………….….7 Figure 1.2………………………………………….….8 Figure 1.3………………………………………….…10 Figure 1.4………………………………………….…11 Figure 1.5………………………………………….…13 Figure 1.6………………………………………….…13 5

ECE 2101L -Experiment 2 Objective: The objective of this experiment is to learn the basic behavior of capacitors and inductors. This includes determination of the equivalent of series and parallel combinations and analyzing steady state behavior of RLC circuits. Pre-Lab Section 1. A series RC circuit has a resistance of 1.0 Mohm and a capacitance of 4.7 uF. What is the time constant? 𝒕 = 1. 0 × 10 6 × 4. 7 × 10 −6 𝒕 = 4. 7 ?𝑒𝑐 2. Determine how long it takes the capacitor to reach full charge for each of the following combinations: a. R=47 ohm, C=47 uF ? = 5𝝉= 5?𝐶 ? = 5 × 47 × 47 × 10 −6 ? = 0. 011045 ?𝑒𝑐 = 11. 045 ??𝑒𝑐 b.) 4.7 Mohm, 𝐶 = 10?? ? = 5𝝉= 5?𝐶 ? = 5 × 4. 7 × 10 −6 × 10 × 10 −12 ? = 0. 000235 ?𝑒𝑐 = 235 µ?𝑒𝑐 3. A series RL circuit has a resistance of 1.0 kohm and an inductance of 1.0 mH. What is the time constant? sec 𝒕 = 𝐿 ? = 1.0×10 −3 1.0×10 3 = 10 −6 ?𝑒𝑐 = 1. 0 µ 6

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B. Lab Section: 1) Measure the DC resistance of the inductors and resistors using the ohms setting on the DMM, recording your readings. Determine and record the theoretical series and parallel combinations. 2) Connect the two capacitors in series and measure the total capacitance using the DMM. Record this value in Table 1.1 under the experimental column. Repeat this process for the remaining combination in Table 1.1. Also determine and record the deviations. 3) Consider the circuit of Figure 1.1 using V1=5V, and . Determine 𝐶 1 = 1µ? 𝐶 2 = 2. 2µ? the voltage across each capacitor and record these values in table 1.2 under Theory. 4) Build the circuit of Figure 1.1 using V1=5V, and .Measure the 𝐶 1 = 1µ? 𝐶 2 = 2. 2µ? voltage across each capacitor and record these values in Table 1.2. Also determine and record the deviation. Table 1.1 Pairing Theory Experimental Deviation 1 F series with 2.2 F µ µ 1.1 µ? N/A N/A 1 F parallel with 2.2 F µ µ 4.4 µ? N/A N/A 7

Total Capacitance = 1 1 1 µ?+ 1 2.2 µ? = 0. 6875 µ? Table 1.2 Voltage Theory Experimental Deviation 𝑉 𝐶1 3.44 V 2.43 V 29.36% 𝑉 𝐶2 1.56 V 1.47 V 5.77% Calculations: 𝑉 𝐶1 = 1 𝐶 1 1 𝐶 1 + 1 𝐶 2 × 𝑉 ? 𝑉 𝐶1 = 1 1 µ? 1 1 µ?+ 1 2.2 µ? × 5𝑉 = 3. 44𝑉 8

𝑉 𝐶1 = 3. 44𝑉 𝑉 𝐶2 = 1 𝐶 2 1 𝐶 1 + 1 𝐶 2 × 𝑉 ? 𝑉 𝐶2 = 1 2.2 µ? 1 1 µ?+ 1 2.2 µ? × 5𝑉 = 1. 56𝑉 𝑉 𝐶2 = 1. 56𝑉 Deviation: % ????? 𝐶 1 = | ?ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒−?𝑥?𝑒?𝑖?𝑒??𝑎? 𝑉𝑎??𝑒 ?ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒 | × 100 % ????? 𝐶 1 = | 3.44𝑉−2.43𝑉 3.44𝑉 | × 100 = 29. 36% % ????? 𝐶 2 = | ?ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒−?𝑥?𝑒?𝑖?𝑒??𝑎? 𝑉𝑎??𝑒 ?ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒 | × 100 % ????? 𝐶 2 = | 1.56𝑉−1.47𝑉 1.56𝑉 | × 100 = 5. 77% RL Circuit 5. Using figure 1.2 with V 1 = 10 V, R = 47kΩ, and L = 10 mH, calculate the time constant and record it in Table 1.3. Also, calculate and record the expected steady state inductor voltage in Table 1.3. 6. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting the resistor and inductor, connect the DMM across the inductor set to read DC voltage (20 volt scale). 7. Connect the power supply to the circuit. The circuit should reach steady state very quickly, in much less than one second. Record the experimental inductor voltage in Table 1.3. Also, compute and record the percent deviation between experimental and theory in Table 1.3. 9

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Table 1.3 𝝉 V L Theory V L Experimental Deviation 0.212 µsec 0 V 0.015 mV + 0.015 mV Table 1.3 Calculations: 𝝉 = 𝐿/? =. 010/47000 = 0. 212µ?𝑒𝑐 RC Circuit 8. Using figure 1.3 with V 1 = 10 V, R 1 = 47kΩ, R 2 = 1kΩ, C = 1µF, calculate the time constant and the expected steady state capacitor voltage and record them in Table 1.4. 9. Set the power supply to 10 V but do not hook it up to the remainder of the circuit. After connecting the resistors and capacitor, connect the DMM across the capacitor set to read DC voltage. 10. Connect the power supply to the circuit. The circuit should reach steady state quickly, in under one second. Record the experimental capacitor voltage and compute the percent deviation between experimental and theory, record these values in Table 1.4. Table 1.4 𝝉 V C Theory V C Experimental Deviation .979 ms 9.79 V 9.62 V 1.74% Table 1.4 Calculations: 𝛕 = ?𝐶 = 1 1 1? + 1 47? × 1µ? =. 979?? V CTheory = 1 1 1? + 1 47? × 10𝑉 = 9. 79𝑉 Percent Error = | 9.79−9.62 9.79 | × 100 = 1. 74% 10

RC Circuit (long time constant) 11. Using figure 1.4 with V 1 = 10V, R 1 = 47kΩ and C = 470µF, calculate the time constant and the expected steady state capacitor voltage, record these values in Table 1.5. 12. Set the power supply to standby, and after waiting a moment for the capacitor to discharge, remove the capacitor and replace it with the 470µF. Connect the DMM across the capacitor. 13. Energize the circuit and record the capacitor voltage every 10 seconds as shown in Table 1.6. This is the charge phase. 14. Remove the power supply from the circuit and record the capacitor voltage every 10 seconds as shown in Table 1.7. This is the discharge phase. 15. Using the data from Tables 1.6 and 1.7, create two plots of capacitor voltage versus time and compare them to the theoretical plots found in the text. 11

Table 1.5 Charging Discharging 𝝉 .979 ms .979 ms V cTHEORY 9.79V 0V Table 1.5 Calculations: 𝛕 = ?𝐶 = 1 1 1? + 1 47? × 1µ? =. 979?? V CTheory = 1 1 1? + 1 47? × 10𝑉 = 9. 79𝑉 Table 1.6 Time (sec) Voltage 0 0 10 0.011 20 0.020 30 0.023 40 0.025 50 0.025 Table 1.7 Time (sec) Voltage 0 .153 10 .127 20 .081 30 .038 40 .014 50 0 12

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Figure 1.5 : Graph of Table 1.6 (Time in Seconds vs. Voltage in Volts) Figure 1.6 : Graph of Table 1.7 (Time in Seconds vs. Voltage in Volts) 13

From these plots, it is comparable to the graphs in the beginning of the text. The shape of the time vs. voltage plot in the charging phase is similar to the sample plot in the text, while the shape of the time vs. voltage plot in the discharging phase is dissimilar, but nevertheless decreasing. Conclusion: In this lab, we observed the steady state characteristics of RC and RL circuits. Capacitors become open circuits, while inductors become short circuits, meaning they become a wire in DC steady state due to their very low resistance. Both components behave as inverses of one another. Once a circuit is charged, the capacitor reaches its final voltage, whereas the inductor reaches zero in the steady state. 14

Postlab: Position 1: V C5 = 0.01µ? 0.01µ?+0.068µ? × 12𝑉 = 1. 5385𝑉 V C6 = 0.047µ? 0.047µ?+0.056µ? × 12𝑉 = 5. 4757𝑉 Position 2: V C5 = 0.022µ? 0.022µ?+0.068µ? × 12𝑉 = 2. 9333𝑉 V C6 = 0.015µ? 0.015µ?+0.056µ? × 12𝑉 = 2. 5352𝑉 Δ𝑉𝐶5 = 2. 9333𝑉 − 1. 5385 = 1. 3948𝑉 Δ𝑉𝐶6 = 2. 5352𝑉 − 5. 4757𝑉 = (− 2. 9405𝑉) 15

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