The Parallel RLC Resonance Circuit

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Lab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:University of AnbarCollege of EngineeringDept. of Electrical EngineeringExperiment No.14The Parallel RLC Resonance CircuitObjectTo perform be familiar with The Parallel RLC Resonance Circuit and theirlaws.Theorythe analysis of a parallel RLC circuits can be a little more mathematicallydifficult than for series RLC circuits so in this tutorial about parallel RLC circuitsonly pure components are assumed in this tutorial to keep things simple.This time instead of the current being common to the circuit components, theapplied voltage is now common to all so we need to find the individual branchcurrents through each element. The total impedance, Z of a parallel RLC circuitis calculated using the current of the circuit similar to that for a DC parallelcircuit, the difference this time is that admittance is used instead of impedance.Consider the parallel RLC circuit illustrated in Figure 1. The AC voltage sourceis( )1

Lab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:University of AnbarCollege of EngineeringDept. of Electrical EngineeringFigure 1. Parallel RLC circuit.Unlike the series RLC circuit, the instantaneous voltages across all three circuitelements R, L, and C are the same, and each voltage is in phase with the currentthrough the resistor. However, the currents through each element will bedifferent.The current in the resistor is.(1)whereThe voltage across the inductor is.(2)which gives.(3)whereandis the inductive reactance.Similarly, the voltage across the capacitor isimplies( )( ), which.(4)2

Lab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:University of AnbarCollege of EngineeringDept. of Electrical Engineeringwhereandis the capacitive reactance.Using Kirchhoff’s junction rule, the total current in the circuit is simply the sumof all three currents.(5)The currents can be represented with the phasor diagram shown in Figure .2Figure .2 Phasor diagram for the parallel RLC circuitFrom the phasor diagram, we see that.(6)and the maximum amplitude of the total current,, can be obtained as3

Lab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:University of AnbarCollege of EngineeringDept. of Electrical Engineering.(7)Note however, since ( ), ( ) and ( )are not in phase with one another,not equal to the sum of the maximum amplitudes of the three currents:is.(8)Withthe (inverse) impedance of the circuit is given by.(9)The relationship between Z, R,andFigure .3 Relationship between Z, R,is shown in Figure .3andin a parallel RLC circuit.From the figure or the phasor diagram shown in Figure .2, we see that the phasecan be obtained as4

University of AnbarCollege of EngineeringDept. of Electrical EngineeringLab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:.(10)The resonance condition for the parallel RLC circuit is given byimplies, which.(11)The resonant frequency is.(12)which is the same as for the series RLC circuit. From Eq. (9), we readily see that1/Z is minimum (or Z is maximum) at resonance. The current in the inductorexactly cancels out the current in the capacitor, so that the total current in thecircuit reaches a minimum, and is equal to the current in the resistor:.(13)As in the series RLC circuit, power is dissipated only through the resistor. Theaverage power is.(14)5

Lab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:University of AnbarCollege of EngineeringDept. of Electrical EngineeringThus, the power factor in this case is.(15)Procedure1. Connect the resistance and inductance in series as shown in Fig.6Fig.42. Adjust the function generator to 200 Hz, 10 V and 50% duty cycle.3. Select sine, waveform, turn the circuit ON for about 50 ms then turn it OFF.4. Measure the phase shift between the current I and the input voltage V usingoscilloscope.5. Draw the result of the display graph.6. Draw the Phasor diagramResonance1. Connect the circuit as shown in Fig. (5).6

Lab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:University of AnbarCollege of EngineeringDept. of Electrical Engineering2. Set the voltmeter to 6 Vrms.3. Select sine waveform; vary the oscillator from 14 kHz to 17 KHz in steps of0.5 kHz.4. Record the reading of the voltmeter at each step as in table (1)5. Evaluate the impedance of the circuit at each step.6. Plot a graph of XL, and Xc w.r.t. of frequency7. Plot a graph of impedance w.r.t. of frequency8. Determine the value of the impedance at the resonant frequoncy.9. Compare the value of the resonant frequency to the theoretical value.Fig. (5).Frequency(kHz)(A)table (1)7

University of AnbarCollege of EngineeringDept. of Electrical EngineeringLab. Name: :fundamental of ElectriccircuitExperiment no.:Lab. Supervisor:Discussion1. Can we obtain a plot of XL, against frequency f experimentally?2. Explain why Phasor and impedance diagrams have the same angles.3. What is the value of Phasor shift if R 300Ω L 400mH with f 50Hz. Discussthe increase or decrease in the phase shift.8

Lab. Supervisor: 1 Experiment No.14 Object To perform be familiar with The Parallel RLC Resonance Circuit and their laws. Theory the analysis of a parallel RLC circuits can be a little more mathematically difficult than for series RLC circuits so in this tutorial about parallel RLC circuits only pure components are assumed in this tutorial to .

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