Electric Circuits Lab
Parallel Resonance
I. Objectives:
After completing this lab experiment using, you should be able to:
1. Observe the effect of frequency on impedance.
2. Observe the effect of Quality factor on parallel resonance.
3. Calculate and verify the resonant frequency in a parallel LC circuit.
4. Identify the phase relation between current and voltage in a parallel LC circuit.
II. Parts List:
1. Resistor (2) 1 Ω, (1) 100 Ω, (1) 500 Ω.
2. Inductor (1) 100 mH.
3. Capacitor (1) 47 nF.
III. Procedures:
Part I:
1. Connect the following circuit in Multisim.
Diagram, schematic Description automatically generated
Figure 1: Parallel LC Circuit
2. Calculate the exact resonant frequency, fr, of the circuit using the flowing equation:
=2.32kHz
3. Calculate the inductive reactance, capacitive reactance, total reactance (XL||XC) impedance magnitude, and phase angle for each frequency shown in Table 1. Ignore the winding resistance for your calculations.
4. Measure and record the resistor voltage for each of the frequencies listed in Table 1.
Frequency
(in Hz)
Calculated
Measured
XL
XC
XT
VR(rms)
700
439.8 Ω
4837.5 Ω
-4397.7
20.589 mV
900
565.5 Ω
3762.5 Ω
-3197.0
14.961 mV
1k
628.3Ω
3386.3 Ω
-2758
12.902 mV
2k
1256.6 Ω
1693.1 Ω
-436.5
2.007 mV
Resonant freq. 2.32k (fr)
(from step 2)
1457.7Ω
1459.6 Ω
-1.9
83.637 uV
3k
1885 Ω
1128.8 Ω
756.2
3.6 mV
5k
3141.6 Ω
677.3 Ω
2464.3
11.64 mV
7k
4398.2 Ω
483.8 Ω
3914.4
18.472 mV
Table 1: Calculated and measured values
5. Draw the frequency response curve from the above results on Plot 1.
6. Connect multimeters or current probes to measure total current or resistor current (IR), inductor current (IL) and capacitor current (IC).
7. Measure and record the rms values for IR, IL, and IC in Table 2.
Frequency (in Hz)
IC
IL
IR
700
2.074 mA
22.663 mA
20.589 mA
900
2.666 mA
17.627 mA
14.961 mA
1k
2.963 mA
15.864 mA
12.902 mA
2k
5.925 mA
7.932 mA
2.007 mA
Resonant freq. (from step 2) 2.32kHz
6.814 mA
6.897 mA
83.637 uA
3k
8.888 mA
5.288 mA
3.6 mA
5k
14.813 mA
3.173 mA
11.64 mA
7k
20.738 mA
2.266 mA
18.472 mA
Table 2: Measured voltage values
8. Draw the current phasor on Plot 2.
Plot 2: Current Phasor
9. Disconnect the digital multimeters from the circuit.
10. Connect the Bode plotter as shown in Figure 2.
Diagram, schematic Description automatically generated
Figure 2. Circuit with Bode Plotter
11. Measure the resonant frequency using the Bode plotter as show in Figure 3.
Graphical user interface Description automatically generated
Figure 3. Bode Plot Output Showing Resonant Frequency
12. Record the resonant frequency for the circuit in Table 3.
13. Calculate the Q factor for the circuit using the following equation.
14. Replace the winding resistor RW with a 100 Ω resistor as shown in Figure 4.
Diagram, schematic Description automatically generated
Figure 4. Parallel Resonant Circuit with RW = 100 Ω
15. Calculate the exact resonant frequency, fr, of the circuit using the flowing equation:
16. Measure and record the resonant frequency for the circuit in Table 3.
17. Calculate the Q factor for the circuit using the following equation.
18. Replace the winding resistor RW with a 500 Ω resistor.
19. Calculate the exact resonant frequency, fr,
20. Measure and record the resonant frequency for the circuit in Table 3.
21. Calculate the Q factor for the circuit using the following equation.