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.