Lab 3 Result Sheet

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University of Alberta *

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209

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Electrical Engineering

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Feb 20, 2024

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ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits Lab 3 Results: Intro to AC Circuits ECE209: Fundamental of Electrical Engineering Name Student ID CCID Harshith rao 1760726 hhrao Maksatbek Abdiev 1775272 abdiev AC Resistor – 100 Ω DMM R 1 (Ω) = 100 ohms Frequency 100 Hz 1 kHz 10 kHz Oscilloscope – Method 1 – Counting Divisions Horizontal - # of divs 4 4 4 SEC/DIV( μ s/div) 2500 250 25 T S – Period ( μ s) 10,000 1000 100 Vertical - # of divs 6.5 6.5 6.5 VOLTS/DIV 2 2 2 V R Pk-Pk – peak-to-peak (V) 13 13 13 Oscilloscope – Method 2 – Cursors T S – Period ( μ s) 10,000 1000 100 fs – Frequency (H Z ) 100 1000 10,000 V R Pk-Pk – peak-to-peak (V) 13 13.2 13.2 Oscilloscope – Method 3 – Automatic Measurements fs –‘ Freq’ (H Z ) 100 1000 10,000 T S – ‘Period’ ( μ s) 10,000 1000 100 V R Pk-Pk – peak-to-peak (V) 12.2 13.2 13.2 V R RMS – ‘Cyc RMS’ (V) 4.21 4.56 4.50 DMM –Milliammeter – RMS current I R RMS - (mA) 42.14 45.62 37.19 Calculate Resistance – (R = V RMS /I RMS ) R ( Ω ) 99.9 99.95 121 AC Capacitor – 1 μF Page 1 of 7

ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits DMM C (nF)= 1006 Frequency f S V C RMS I C RMS X C C (Hz) (Hz) (V) (mA) (Ω) (nF) 100 Hz 100 7.55 4.70 1606.38 990.8 1 kHz 1000 7.01 43.25 162.08 982 10 kHz 10,000 1.74 86.5 20.11 791 a) Show your work for finding X C and C at 100Hz frequency. XC= VC/IC XC=1/2pi*f*C 7.55/4.70*10^-3 C= 1/2PI*F*XC 1606.38 C= 1/2pi*100*1606.38= 9.91*10^-7= 990.8 AC Inductor – 2.5 mH DMM R L1 (Ω)= 8 Frequenc y f S V L RMS I L RMS Z L X L L (Hz) (Hz) (V) (mA) (Ω) (Ω) (mH) 100 Hz 100 0.813 100.2 8.114 1.36 2.15 1 kHz 1000 1.85 98 18.88 17.1 2.72 10 kHz 10,000 6.80 37.91 179.37 179.2 2.85 b) Show your work for finding XL, ZL and L at 1000Hz frequency. 1000hz ZL= VL/IL XL=2pi*f*L 1.85/98*10^-3= 18.88 OHMS L= XL/2pi*f = 17.1/2pi*1000 XL=sqrt(R^2-ZL^2)= sqrt(18.88^2-8^(2) = 17.1ohms L= 0.00272*1000=2.72mH Page 2 of 7

ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits Series RC Circuit c) Show your work for finding R, X C , C and Z at 1.592 kHz. Compare your calculated impedance value with pre lab calculated impedance. Does values are same or different? Frequency (Hz) 100 Hz 1 kHz 1.592 kHz 10 kHz fs –‘ Freq’ (H Z ) 100 1000 1592 10,000 T S – Period (μs) 10,000 1000 627 100 V s RMS (V) 7.52 6.22 5.56 4.55 V C RMS (V) 7.54 5.28 3.94 0.729 I s RMS (mA) 4.67 32.39 38.32 36.54 V R RMS (V) 0.48 3.29 3.89 4.47 Calculations R -( ohms law) (Ω) 102.7 101.57 101.51 122.33 X C -( ohms law) (Ω) 1614.56 163 102.8 19.95 C (μF) 0.99 0.98 0.972 0.797 Z-(ohms law) (Ω) 1610.28 192.03 145.1 124.52 Fs= 1.592= 1592hz R= VR/IS=3.89/0.03832 = 101.51ohms XC= OHMS LAW= VC/IS =3.94/0.03832=102.81ohms C= 1/2pi*f*XC = 1/2pi*1592*102.81=0.972microfarads Z= ohms law Vs/is 5.56/0.03832=145.1 Page 3 of 7

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ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits Prelab impedance 159 here its lower due to experimental error Series RL Circuit d) Show your work for finding R, Z L , X L , L and Z at 6.370 kHz. R=VR/IS= 3.68/35.43*10^-3 Fs= 6.370khz= 6370hz R= 103.87ohms ZL= VL/IS = 3.88/ 35.43*10^-3 L=Xl/2pi*f 109.51 ohms 109.21/ 2pi*6370 XL= sqrt(zl^2-rl^2) = 109.21 L=0.00272=2.73mH Z= vs/is= 5.59/35.43*10^-3= 157.78 Frequency (Hz) 100 Hz 1 kHz 6.370 kHz 10 kHz fs –‘ Freq’ (H Z ) 100 1000 6370 10,000 T S – Period (μs) 10,000 1000 157 100 V s RMS (V) 4.66 4.72 5.59 6.15 V L RMS (V) 0.35 0.81 3.88 5.13 Page 4 of 7

ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits I s RMS (mA) 43.5 43.37 35.43 28.76 V R RMS (V) 4.34 4.33 3.68 3.12 Calculations R -(ohms law) (Ω) 99.77 99.84 103.87 108.48 Z L -(ohms law) (Ω) 8.05 18.68 109.51 178.37 X L (Ω) 0.895 16.87 109.21 178.2 L (mH) 1.43 2.69 2.73 2.84 Z- -(ohms law) (Ω) 107.13 108.83 157.78 213.83 Impedance-Frequency Plot The following pages have been left for you to include the plots that you are required to create as part of your post-lab. To create your plots you can use whichever software you would like (Excel, Matlab, etc.) export your plot as an image and import it into your Lab 3 - Results sheet in the appropriate place. Your plots should include: · A Plot title · Label your axes and show what unit of measure is used. · Include a marking for your data-points. · Include a line between your data-points in the same series. · Include a legend. · Make sure your scales are appropriate and visible. < Insert your plot here > Using your measurements and calculations from the AC Resistors, Capacitor and Inductor sections, plot each components resistance/reactance vs. frequency on the Page 5 of 7

ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits same plot. Plot both the inductors reactance as well as its non-ideal impedance. Use a logarithmic scale for both the x-axis and y-axis. 1) Make some general observations and conclusions about how each of the different components on the plot Impedance-Frequency of R, L and C behave. For the resistor the graph is a straight line with a positive gradient and the resistance is almost constant with change in frequency eg the slope doesn’t change by much For c the graph is a graph with a negative gradient indicating decrease in capacitance with increase in frequency For L the graph is a curve with increasing positive gradient Page 6 of 7

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ECE209 – Fundamentals of Electrical Engineering Lab 3: Intro to AC Circuits 2) Looking at your results, does the inductor behave more like an ideal component at 100Hz or at 10 kHz? At 100khz as the all the graphs are linear with a positive gradient Page 7 of 7