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ELEC 273

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Electrical Engineering

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Jan 9, 2024

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LABORATORY REPORT Basic Circuits & Systems Laboratory This cover page must always be the top sheet Course: ELEC 273 275 Lab Section: ( Circle ) Experiment No.: Date Performed: 20 – – YYYY – MM – DD Experiment Title: Name: ID No.: Lab Partner Name: Lab Partner ID: I certify that this submission is my original work and meets the Faculty’s Expectations of Originality Signature: Date: 20 – – YYYY – MM – DD FL-X Prince Raphael Johnson 40153375 Faisal Quraishi 40161298 23 10 11 #4 Measurement of AC Power 23 11 20

Abstract The objective of this experiment was for the students to familiarize themselves with the measurement of AC power being delivered to a resistive load, an RC load, as well as an RL load. This will be done using a Multi-Function Digital Meter, a Wattmeter as well as an AC Voltage Source Introduction Just like previously, this experiment will revolve around AC measurements, in this case AC power. The AC circuit will be the equivalent of a DC circuit, with the impedance being equivalent to the resistance in this context (and measured in ohms) as well as the inductance and the capacitance. The Digital meter used during the experiment will be reading the RMS voltage across the various loads as well as the RMS current flowing through them. Procedure (Methods) For the various tasks, always 1 st make sure that Variac knob is at its zero position and never leave the R control knob at 0 to avoid making the load 0 ohms and possibly blowing the fuse in the load unit when power is applied Power Measurement - 1 st calibrate the rheostat in the RL load unit using the ohmmeter to get the resistance at each dial - Proceed to connect the RL unit, have the R dial to 40 and slowly increase the Variac setting until the meter reads about 1 A. From there, we get the value of the voltage, current, power and power factor and increase R afterward to get the next values for the different Resistive loads - Repeat the same process for RL and RC load but have the R dial to 10 1 st . In the case of the RC load, do not forget to disconnect the inductance of the RL load unit and set up the RC load by connecting the resistor in the RL load unit in series with the C load unit. Power Factor Compensation - Here, with the Variac again set to 0, we set up the circuit between the capacitor load unit (with all the switches down at 1 st ) and the RC unit and have the R dial set to 30. Again, slowly increase the Variac setting until the meter reads about 1 A - 1 st record the voltage, current and power with the capacitance set to 𝐶 = 0, then successively switch in C values from 1 µF to 40 µF and proceed to record the voltage, current and power values as 𝐶 is increased Results and Discussion Power Measurement - Does the measured value of the power factor agree with the theoretical value? - We have the theoretical 𝑝𝑓 = cos 𝜃 , with 𝜃 = tan-1 ( 𝜔 L/R) for the RL load and 𝜃 = tan -1 (- 1 ωC 𝑅 ) for the RC load o At 60Hz, for the RL load, 𝜔 L= 2π60*0.204H  For R= 40, 𝜃 = 62.52° / For R=60, 𝜃 = 52.04°/ For R= 80, 𝜃 =43.87°

o At 60Hz, for the RC load, 𝜔 C= 2π60*(40*10 -6 F)  For R= 10, 𝜃 = -81.425° / For R=30, 𝜃 = -65.659°  For R= 50, 𝜃 = -52.984° - The calculated pfs for the resistive load were not far from the measured power factor as demonstrated by the % error, which was not the case for either the RL or RC load who’s calculated pfs were very far from the measured ones. In that case, the calculated pfs for the RL or RC load were closer to the measured pf of the resistive load actually. R Load Measured RMS Voltage 𝑉 rms Measured RMS Current 𝐼 rms Measured average power ? Measure d power factor 𝑝𝑓 Calculated 𝑝𝑓 = ? / (𝑉 rms * 𝐼 rms ) Theoretical Power factor 𝑝𝑓 = cos 𝜃 % error in the measured power factor compared to the calculated value R=40 Ω 34 0.89 30.6 W 1.0 1.011 0 -1.1% R=60 34.1 0.58 19.8 1.0 1.001 0 -0.1% R=80 34.3 0.43 14.7 1.0 0.9966 0 0.34% RL load 204 mH R=10 98.8 0.89 A 88.2 0.23 1.003 cos(62.52°) = 0.461 -336% R=30 98.7 0.83 81.9 0.39 0.99974 cos(52.04) = 0.615 -179.3% R=50 98.8 0.77 76 0.59 0.9990 cos(43.87) = 0.721 -69.32% RC Load 40 µF R=10 56.4 0.89 49.7 0.07 0.9901 cos(-81.425°) = 0.149 -1314.4% R=30 56.2 0.80 44.9 0.36 0.9987 cos(-65.659°) = 0.412 -177.42% R=50 56.3 0.69 38.9 0.55 1.001 cos(-52.984°) = 0.602 -82%

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Load Measured Apparent power ? APP = 𝑉 rms 𝐼 rms (watts) Measured power factor 𝑝𝑓 Measured Angle 𝜃 =±cos -1 ( 𝑝𝑓 ) Theoretica l Angle of the impedance 𝜃 Reactive power ? = ? AP sin 𝜃 (vars) Complex power 𝑆 = ? + 𝑗? % error in angle 𝜃 RL load R= 40 P=98.8*0.89 = 87.932 0.23 +cos -1 (0.23) = 76.70° = 62.52° Q= 87.932sin (76.70) = 85.57 87.932+j85.57 18.49% R= 60 98.7*0.83 = 81.921 0.39 = 67.05° = 52.04° = 75.44 81.921+j75.44 22.39% R= 80 98.8*0.77 = 76.076 0.59 = 53.84° = 43.87° = 61.42 76.076+j61.42 18.52% RC load R= 10 56.4*0.89 = 50.196 0.07 -cos -1 (0.07) = 85.99° = -81.425° = 50.07 50.196 + 50.07 195% R= 30 56.2*0.80 = 44.96 0.36 = 68.90° = -65.659° = 41.95 44.96+j41.95 195% R= 50 56.3*0.69 = 38.847 0.55 = 56.63° = -52.984° = 32.44 38.847+j32.44 194% - As seen in the table, the measured angles for the impedances does not agree at all with the theoretical values of 𝜃 for the RL load and 𝜃 for the RC load. For the RL Load, the theoretical values were not completely far off, but that was not the case the RC load as the theoretical values were all negative Power Factor Correction Measured RMS Voltage 𝑉 rms Measured RMS Current 𝐼 rms Measured average power ? Measured power factor 𝑝𝑓 Calculated Power Factor pf % error 𝐶 = 0 𝜇𝐹 104.7 V 0.89 A 94.7 W 0.39 94.7/(104.7*0.89) = 1.016 -160% 𝐶 = 5 𝜇𝐹 105.6 0.71 79.7 0.49 = 1.063 -117% 𝐶 = 10 𝜇𝐹 105.9 0.51 53.6 0.65 = 0.992 -53% 𝐶 = 15 𝜇𝐹 105.5 0.36 38.0 0.92 = 1.001 -9% 𝐶 = 20 𝜇𝐹 106.2 0.29 31.8 0.97 = 1.033 -6.5% 𝐶 = 25 𝜇𝐹 105.7 0.34 36.0 0.66 = 1.002 -52% 𝐶 = 30 𝜇𝐹 106.6 0.48 51.1 0.43 = 0.999 -132% 𝐶 = 35 𝜇𝐹 106.0 0.66 70.0 0.31 = 1.001 -223% 𝐶 = 40 𝜇𝐹 106.1 0.85 89.0 0.23 = 0.987 -329% 𝐶 for minimum current, 𝐶 = 20 𝜇𝐹 106.2 0.29 31.8 0.97 1.033 -6.5%

- For each capacitance value, the power factor is calculated using 𝑝𝑓 = ? / (𝑉 rms * 𝐼 rms ) - For 𝐶 = 0 𝜇𝐹 , the power factor is similar the measured one with the RL circuit for R=60 Ω - For minimum current, we used c=29.52 µF, R=33 Ω , and in this case the current flowing out of the generator using the LTSpice circuit is 0.584877A, which does not agree with the measured current for similar value, but it is not far from it. - The power factor from the LTSpice simulation done in the prelab does not agree with the one we measured during the lab itself. Does the value agree with your measurement? Conclusion Overall, the goal of this experiment was met, and it was useful for students to get familiar with AC power measurement and calculations. Some of the results we got in the report varied widely from the one measured during the lab, but it did show us that despite doing well during the lab and every being correct, there will still be some differences when it comes to the report and the actual theoretical calculations and value.