I need help to fill out table 3 on page 88, and question 1 to 3 on page 89 to 90

Vo Monitor Run Monktor Run Output Voltage, Ch 01 (v) Output Voltage, Ch 01 (v) IbWNNOHNWI -3 -2 - 1 1 0.0001 0.0002 0.0003 0.0004 0.0005 Voltage, Ch Ctv) Time (s) [Scope title here] [Graph title here] Monitor Run 2.5 3686.523 Hz, 1.571 V Squad Ever! " 2.0 Voltage, Ch C () 1.5 :-- 1.0 0.5 2000 4000 6000 8000 1000 0 Frequency (Hz) [FFT title here]6 3.980x10-" s. 4.962 V 0.006 s. 0.968 V Vo Vo V MIC 5 . 8000HZ 4 500Hz . A 0.006480 s. 4.968 v N 4.120x10-" s. 2.590 V AN ON A O O Voltage, Ch C (V) Output Voltage, Ch 01 (v) Output Voltage, Ch 01 (v) Voltage, Ch c (V) N JOHNWA N ab 0.00036 0.00038 0.00040 0.00042 0.00044 0.00046 0.0050 0.0055 0.0060 0.0065 0.0070 0.0075 Time (s) Time (s) [Graph title here] (Graph title here] 9.540x10-" s. 3.235 V- vo 3.0 Fres Theory 9.600x10* s. 4.970 V 2.5 ver 2.0 Output Voltage, Ch 01 (v) Voltage, Ch C (V 1.5 1.0 0.5 0.0 0.00090 0.00092 0.00094 0.00096 0.00098 0.00100 0.00102 Time (s) [ Graph title here] 6 2Experiment 8.1 Series LCR resonance Purpose Study resonance in a series inductor-capacitor-resistor (LCR) circuit by examining the voltage across the resistor as a function of frequency of the applied sine wave. Equipment L-C-R board with L = 3.3 mH, C =0.68 UF, R = 100 $, PASCO 850 interface, one voltage sensor (PASCO UI-5100), computer. Theory 1. Sinusoidal voltage and current (a) Alternating voltage: U= V. sin(@t + 8,), U-- instantaneous value of the voltage, Vo -- peak value of the voltage, do -- phase angle of U, @=2nf, T=1/ f , units: @ (rad/s), f (Hz = 1/s). (b) Alternating current: i = I, sin(wt + 4,) 2. Phasor i = 1, sin(wt+ 4,) w (a) A graphic representation of a sinusoidal quantity (such as an alternating voltage or current). (b) Phasors rotate counterclockwise about the common origin with constant angular velocity W. c) The magnitude of a phasor equals the peak value of the Horizontal and sinusoidal quantity. vertical reference lines 'd) The vertical component of a phasor gives the instantaneous Figure 1 Phasor of alternating current value of the sinusoidal quantity. e) Purpose: to simplify the addition of two or more sinusoidal functions such as: U = UR +U, + Uc = VR sin(wt) + V, sin(wt +90) + Vc sin(wt -90) = ? It is much easier to add two or three sinusoidal functions using phasor diagram! 3. Phasor diagram of a resistor in ac circuits VR R UR = VR sin ct, iR = IR sin cot, VR = IRR, (a) UR and iR are in phase 4. Phasor diagram of an ideal inductor in ac circuits (Note: An "ideal" inductor" has no resistance) L U1 = VL sin wt, iz = 1, sin(wt -90), (b) V1 = I,XL, XL = WL --- inductive reactance ($2) (1) iz lags UL by 90 or UL leads iz by 90%. 5. Phasor diagram of a capacitor in ac circuits UC = Vc sin wt, ic = Ic sin(wt +90) (c) Vc = IcXc, XC =- -- capacitive reactance ($2) (2) ic leads Uc by 90 or vc lags ic by 90%. Figure 2 Phasor diagram for a pure (a) resistor, (b) inductor, (c) capacitor in ac circuit. 79U1 = V, sin(cut +90') U . = V . sin(@t -90') UR = VR sin cl M 6. Series LCR circuit diagram Figure 3 shows L, C, R and an AC R L C power supply in series connection. Signal generator 1 = 10 sin of U = V. sin (wt + () Figure 3 Series LCR circuit diagram 7. Phasor diagram of series LCR circuit For series R-L-C circuit we have: i = ip = 1, = ic = I, sin wt U = V. sin(ct + Vo = VVB + (V - Vc)? = 10VR2 + ( X, - Xc)? = 1.Z (4 ) where Z = \\R' +(X, -Xc) (the impedance of LCR circuit). (5) The angle @ can also be determined from the phasor diagram: cos @ = -, or tang = - ( X 1 - XC) V -V (6) R (p is the phase angle between i & U). VR If X, > Xc, 420, u leads i by p. If X, Wres = 7 LC (7) W pes circuit (with V, > Vc ) .: Wres = 2nt fres =- .. > fres = = Wres = VLC 27VLC (8) Z = \\R2 + (X, - Xc)? = R=Zmin (9) To =Z R Vo = Vo = In , = tan-I AL- AC = tan-(0) =00 (10) R " X 1 = Xc :. I.X, = 1.Xc ->V. = Vc. (but U, =-vc) (11) I (A) Note: At resonance, X1 = Xc, Z = Zmin = R, I. = Imax = Vo IR, os 200 9 p=0, i.e., the current i(t) and voltage U(t) are in phase, and 04 VR = VRmax = Vo . These results are derived based on an 0.3 assumption: the inductor is ideal which has only inductive reactance without resistance. In practice, any real inductor has resistance and therefore at resonance VR = VRmax f {theory} Repeat all the three steps in Measurement #1 but with the following two changes. l. in step 2, in the Signal Generator panel change the Frequency from fraheary) to 8000 Hz. 2. Rename Run #N as \"8000 Hz". When all the three measurements are done, set \"Amplitude: 0 V\6. Calculate Pexp and theory at the three frequencies listed in Table 3. The details of your calculations on Pexp and theory will be the answers to question 1 in the section of "Questions and exercises". Table 3 Comparison of Pexp with theory f = 500 Hz f = fres (theory) f = 8000 Hz At = t(UR) -1(0) = Pexp = WAt = 2nf At Ptheory = tan- X, -X R 7. Setup a Text Box on Workbook Page #1 and type in content similar to that in Fig. 10. (Use step 4 in Data Analysis of Exp 8.1). B. Your Workbook Page #1 should be similar to Fig. 10 in which the red and blue curves correspond to UR (1) and U(t) curves respectively. 1.5 -0.008102 5. 0 978 V 0.008498 5. 4.930 V- 1.0 -D.009 5. 3.292 V 0.009 . 4 986 V A Voltage, CHA() A Output Voltage. Ch 01 (V) A voltage Cha() Output Voltage. Ch OL (V) 500 M2 0 68 mi 3940 Hz 0.same 0.0075 0.0080 0.0085 0.0090 0.0095 Time (s) D.00895 0.00900 0.00905 0.00910 0 00915 00920 0.009250 00930 Time (s) (Graph title here] [Graph title here) A 296 , $ 9106090 0 009894 5. 2.571 V Experiment 8.2 Phase angle vs frequency L = 3.3 mH, C = 0.68 HF, R = 100 02 A voltage. Ch AM) A Output Voltage, Chol (V) Lab date: Lab section: Name Lab TA signature: 8000 MZ 0.68md 1 7 0.009800.00982 0.00984 0 00985 0.00968 0.00990 0.00992 0.00994 0.00996 Time (al Figure 10 Data from Experiment 8.2 Phase angle vs frequency Work to be done: 1. Print Workbook Page #1 (similar to Fig. 10): Click "Print" icon in the Tool Bar, select # of pages to be printed, click "print" at the bottom. 2. Let your TA check your Page #1, if it is OK your TA will sign it. Caution: Make sure that your printed Workbook Page #1 is OK before you close the Capstone. All the data collected in Experiment 8.2 will be lost when the Capstone is closed! 3. Close PASCO Capstone by clicking the red-cross at the upper corner, then select "discard". 4. Turn off PASCO 850 interface and shut down the computer. 5. Clean up your bench. 88