Lab 17 Series Resonance on line Ala LM 17Mar2020 rev1 (1)

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Lab 17 (eBook 26) Series Resonance Name ____________________ Date ___________________ Class ___________________ READING Text, Sections 13–1 through 13–4 OBJECTIVES After performing this experiment, you will be able to: 1. Compute the resonant frequency, Q , and bandwidth of a series resonant circuit. 2. Measure the parameters listed in objective 1. 3. Explain the factors affecting the selectivity of a series resonant circuit. MATERIALS NEEDED Resistors: One 100 Ω, one 47 Ω One 0.1 μF capacitor (changed from original 0.01 μF to match figure 17-3) One 100 mH inductor REQUIRED LAB PREPARATION (PRELAB) 1. Read all sections of the lab. 2. READ document named “BRIGHTSPACE ON-LINE LAB ASSIGNMENT AND SUBMISSION PROCEDURE” available in Lab 11 folder 3. Read the text book, sections 13-1 through 13-4 4. Find the required resistors, capacitors and inductor for this lab as indicated in the Materials Needed section above 5. Review the oscilloscope “time base operation” or what is called Horizontal Control depending on the oscilloscope manufacturer. 6. Review the relationship between frequency and period, what is the period at 2KHz? What should the time/div be set to on the oscilloscope to show 1 cycle on the full screen? ANS: _______________ Lab 17 P a g e | 1

7. Complete the PreLab questions at the back of this document and hand in to teacher before going to your Lab station. SUMMARY OF THEORY The reactance of inductors increases with frequency according to the equation X L = 2π fL On the other hand, the reactance of capacitors decreases with frequency according to the equation Consider the series LC circuit shown in Figure 17–1(a) . In any LC circuit, there is a frequency at which the inductive reactance is equal to the capacitive reactance . The point at which there is equal and opposite reactance is called resonance . By setting X L = X C , substituting the relations given above, and solving for f , it is easy to show that the resonant frequency of an LC circuit is where f r is the resonant frequency . Recall that reactance phasors for inductors and capacitors are drawn in opposite directions because of the opposite phase shift that occurs between inductors and capacitors. At series resonance these two phasors are added and cancel each other . This is illustrated in Figure 17–1(b) . The current in the circuit is limited only by the total resistance of the circuit . The current in this example is 5.0 mA. If each of the impedance phasors is multiplied by this current, the result is the voltage phasor diagram as shown in Figure 17– 1(c) . Notice that the voltage across the inductor and the capacitor can be greater than the applied voltage! Figure 17–1 Lab 17 P a g e | 2

At the resonant frequency, the cancellation of the inductive and capacitive phasors leaves only the resistive phasor to limit the current in the circuit. Therefore, at resonance, the impedance of the circuit is a minimum and the current is a maximum and equal to V S / R . The phase angle between the source voltage and current is zero. If the frequency is lowered, the inductive reactance will be smaller and the capacitive reactance will be larger. The circuit is said to be capacitive because the source current leads the source voltage. If the frequency is raised, the inductive reactance increases, and the capacitive reactance decreases. The circuit is said to be inductive. The selectivity of a resonant circuit describes how the circuit responds to a group of frequencies . A highly selective circuit responds to a narrow group of frequencies and rejects other frequencies. The bandwidth of a resonant circuit is the frequency range at which the current is 70.7% of the maximum current . A highly selective circuit thus has a narrow bandwidth. The sharpness of the response to the frequencies is determined by the circuit Q . The Q for a series resonant circuit is the reactive power in either the coil or capacitor divided by the true power, which is dissipated in the total resistance of the circuit . The bandwidth and resonant frequency can be shown to be related to the circuit Q by the equation Figure 17–2 illustrates how the bandwidth can change with Q . Responses 1 and 2 have the same resonant frequency but different bandwidths. The bandwidth for curve 1 is shown. Response curve 2 has a higher Q and a smaller BW . A useful equation that relates the circuit resistance, capacitance, and inductance to Q is Figure 17–2 Lab 17 P a g e | 3

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The value of R in this equation is the total equivalent series resistance in the circuit. Using this equation, the circuit response can be tailored to the application. For a highly selective circuit, the circuit resistance is held to a minimum and the L/C ratio is made high. The Q of a resonant circuit can also be computed from the equation where X L is the inductive reactance and R is again the total equivalent series resistance of the circuit. The result is the same if X C is used in the equation, since the values are the same at resonance, but usually X L is shown because the resistance of the inductor is frequently the dominant resistance of the circuit . PROCEDURE 1. See document titled” BRIGHTSPACE assignment and submissions process” which is available in Lab 11 folder, 2. These include a. Simulate the circuit in Multisim and record the required results in the appropriate table, b. Paste into a blank sheet an image of your actual breadboard as if you were doing the experiment in the Lab, and c. Submit this completed Lab document, and the simulation files via the assignment folder in Brightspace. 3. Use the Multisim spec values for all your calculation, and read the yellow highlighted comments in table below. Lab 17 P a g e | 4

Table 17–1 Listed Value Measured Value L 1 100 mH XXXXXXXXXXXXXXXXXXXXXX C 1 0.1 μF XXXXXXXXXXXXXXXXXXXXXX R 1 100 Ω Do not use R 1 in Multism Do use R 1 on your breadboard which you will photographe and then copy pasted into this document. R S 1 47 Ω XXXXXXXXXXXXXXXXXXXXXX R W ( L 1 resistance) XXXXXXXXXXXXXXXXXXXXXX Figure 17–3 COPY/PASTE image of your Breadboard here; Lab 17 P a g e | 5

4. Capture in Multisim the schematic shown in Figure 17–3 excluding R 1 . The purpose of the parallel 100 Ω resistor is to reduce the Thevenin driving impedance of the generator and, therefore, the total equivalent series resistance of the circuit. 1 Compute the total resistance of the equivalent series circuit. Note that looking back to the generator, R TH is in parallel with R 1 . In equation form, the equivalent series resistance, R T , is R T = ( R TH || R 1 ) + R W + R S 1 6. Enter the computed total resistance in Table 17–2 . 7. Paragraph left blank Table 17–2 Computed Measured R T 47ohm f r 1.59hz 1.6 Q 21 V RS1 940mv f 2 1.629khz Lab 17 P a g e | 6

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f 1 1.54khz BW 0.89HZ 0.089hz 8. Using the measured values from Table 17–1 , compute the resonant frequency of the circuit from the equation: 8. Record the computed resonant frequency in Table 17–2 . 9. Use the total resistance computed in step 3 and the measured values of L and C to compute the approximate Q of the circuit from the equation: 10. Enter the computed Q in Table 17–2 . Compute the bandwidth from the equation: 11. Enter this as the computed BW in Table 17–2 . 12. Using your Multisim oscilloscope, tune for resonance (ie vary the frequency of the signal generator) by observing the voltage across the sense resistor, RS1. As explained in the text, the current in the circuit rises to a maximum at resonance. The sense resistor will have the highest voltage across it at resonance . Measure the resonant frequency with the oscilloscope. Record the measured resonant frequency in Table 17–2 . 13. Now that you have the resonance frequency, verify that the voltage across R 1 or Vs (if R 1 was not used) is set to 1.0 V pp . Next, measure the peak-to-peak voltage across the sense resistor at resonance. The voltage across R S 1 is directly proportional to the current in the series LC branch, so it is not necessary to compute the current. Record in Table 17–2 the measured peak-to-peak voltage across R S 1 ( V RS 1 ). 14. Raise the frequency of the generator until the voltage across R S 1 falls to 70.7% of the value read in step 7. This means that the Thevenin resistance of the generator is included in the measurement Lab 17 P a g e | 7

of the bandwidth. Measure and record this frequency as f 2 in Table 17– 2 . 15. Lower the frequency to below resonance until the voltage across R S 1 falls to 70.7% of the value read in step 7 . Again, do not adjust the generator amplitude . Measure and record this frequency as f 1 in Table 17–2 . 16. Compute the bandwidth by subtracting f 1 from f 2 . Enter this result in Table 17–2 as the measured bandwidth. 17. At resonance, the current in the circuit, the voltage across the capacitor, and the voltage across the inductor are all at a maximum value. Tune across resonance by observing the voltage across the capacitor, then try it on the inductor. Use the oscilloscope difference function technique described in Experiment 8 What is the maximum voltage observed on the capacitor? Is it the same or different than the maximum voltage across the inductor? Indicate your answer next to the measured V. 18. Due to the Low Frequency of this resonant circuit, instead of doing scope differential measurement you could connect two DMMs across L and C, and resonance will be when both DMMs measure exactly the same voltage. V C (max) = _________ V L (max) = _________ CONCLUSION: Lab 17 P a g e | 8

EVALUATION AND REVIEW QUESTIONS 1. (a) Compute the percent difference between the computed and measured bandwidth from Table 17-2. (b) What factors account for the difference between the computed and measured values? 2. (a) What is the total impedance of the experimental circuit at resonance in each of the two sections of this Lab? ____________________ (b) How do the two resonant frequencies compare and why? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ c) What is the phase shift between the total current and voltage at resonance? _______________________________________________________________ 3. (a) In step 12, you measured for the first time, the maximum voltage across the capacitor and the inductor. The maximum voltage across either one should have been larger than the source voltage. How do you explain the presence of this voltage greater than the source voltage? Lab 17 P a g e | 9

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(b) Is this a valid technique for finding the resonant frequency? ___________________ 4. (a) What happens to the resonant frequency, if the inductor is twice as large and the capacitor is half as large? ________________ (b) What happens to the bandwidth? 5. (a) Compute the resonant frequency for a circuit consisting of a 50 μH inductor in series with a 1000 pF capacitor. f r = ______________ (b) If the total resistance of the above circuit is 10 Ω, what are Q and the bandwidth? Q = _________________ BW = ________________ Lab 17 P a g e | 10

Lab 17, Series RLC Resonance PRE-LAB Complete the PreLab questions at the back of this document and hand in to teacher before going to your Lab station. Name ___NEELMANI_________________ Date ___________________ Class ___________________ 1. Explain what “resonance” means when you have an inductor and capacitor in series. For series RLC circuit, resonance frequency is the frequency at which the impedance of the circuit is at a minimum or the frequency at which the impedance is purely real (that is purely resistive). 2. How do the capacitor and inductor behave in a series RLC circuit (think of vector directions). Capacitor Is source of reactive power and inductors is sink of reactive power this is the basic of inductor and capacitor in any electrical circuit. 3. What is the formula for resonant frequency using L and C? Fr =1/2x3.14 (LC) 1/2 Lab 17 P a g e | 11

4. What does it mean when a circuit is considered Capacitive? Same question for an Inductive circuit? IN THE RLC CIRCUIT WHEN THE CAPACITOR VOLTAGE LEADS THE INDUCTOR VOLTAGE IN THE CIRCUIT . IT IS CALLED AS CAPACITIVE. Whereas WHEN THE INDUCTOR VOLTAGE LEADS IT IS CALLED INDUCTIVE. 5. Given a resonant frequency f r , when would the circuit be considered as Capacitive? WHEN IT VOLTAGE LEADS THE CIRCUIT. 6. Following Q5 above, when would the circuit is considered Inductive? WHEN INDUCTOR VOLTAGE LEADS. 7. What is the total impedance of an RLC circuit at resonance? Xt = XL-XC Z= (R 2 +Xt 2 ) 1/2 8. In Fig 17-1 (c) on page 2, why is the voltage vectors of L and C equal to 15V. Answer using math and Ohm’s Law. Lab 17 P a g e | 12

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9. At the resonant frequency of an LRC circuit, what is the total current being consumed? Answer using math and Ohm’s Law. I= V/R 10. What is the meaning of Bandwidth (BW) with respect to the resonant frequency? What are the characteristics of BW? 11. What is Q in a resonant circuit? Qis the quality of resonant circuit. 12. Write at least 2 formulas to calculate Q. 13. How does Q vary vs BW? 14. What is the total power consumed at resonance? Show your math. Lab 17 P a g e | 13

Lab 17 P a g e | 14