AC Parallel RLC Circuit

DeVry University

College of Engineering and Information Sciences

OBJECTIVES

To analyze a parallel AC circuit containing a resistor (R), an inductor (L), and a capacitor (C).
To simulate the RLC circuit and observe the circuit responses.
To build the RLC circuit and measure the circuit responses.

II. PARTS LIST

Equipment:
IBM PC or Compatible
Function Generator
DMM (Digital Multimeter)
Parts:
1 – 470 Ω Resistor 1 – 1 µF Capacitor
1 – 47 mH Inductor

Software:
MultiSim 11

III. PROCEDURE

A.
Theoretical Analysis

Given the R, L, & C parallel circuit in Figure 1, calculate the total equivalent admittance, YT, and the impedance, ZT, of the circuit at f = 550 Hz and 1 kHz. List the calculated values in Table 1.
AC

C = 1 µF

R = 470 Ω

IS

f = 550 Hz

IL

IR

IC

+

Function Generator

RL

L = 47 mH

VS = 2.5 VRMS

Function
Generator
V
S
= 2.5 V
RMS
C

=

1

µ
F
R

=

4
7
0

Ω
I
R
I
C
+
I
S
f = 550 Hz
I
L
L

=

4
7

m
H
R
L
Function
Generator
V
S
=
2
.
5
V
RMS
C

=

1

µ
F
R

=

4
7
0

?
I
R
I
C
+
I
S
f
=
550
Hz
I
L
L

=

4
7

m
H
R
L

Figure 1: Parallel R, C, L Circuit

Frequency
Hz

L & C
Admittances in Rectangular Form

Inductor

G
L
– jB
L

Capacitor

G
C

+
jB
C

550

1000

Frequency
Hz

Total Circuit Admittance Y
T

Rectangular Form

G
T
+ jB
T

Magnitude

Angle

550

1000

Frequency
Hz

Total Circuit Impedance Z
T

Rectangular Form

R
T
+ jX
T

Magnitude

Angle

550

1000

Table 1 – Calculated
RLC
Admittance and Impedance Values

Calculate and record the following quantities:

Frequency
Hz

I
R
(RMS). A

I
C
(RMS), A

I
L
(RMS). A

Magnitude
Angle
Magnitude
Angle
Magnitude
Angle
550

1000

Frequency
Hz

{I
R

+ I
C
+ I
L
}= I
S
(RMS), A

I
S
= V * Y
T

Rectangular Form
Magnitude
Angle
Magnitude
Angle
550

1000

Table 2 – Calculated RLC Component Current Values

Does the sum of the magnitudes of the three currents IR, IC, and IL, in the table above, equal the current, IS, calculated directly in the last column?

(YES or NO)

Explain why your answer is what it is.
Calculate the power dissipated by the parallel resistor and the power supplied by the source:

Frequency Hz

P
R
, W

P
S
, W
550

1000

Table 3 – Calculated RLC Resistor Power Dissipation

B
.
Multisim

Simulat
ion and
Circuit Calculations

Launch MultiSim and build the circuit schematic shown in Fig
ure

2. Include the AC Power source and the DMMs.

Set both DMMs, XMM1 thru’ XMM4, to read AC measurements and Current, I. See fig. 2 below.

Figure 2: MultiSim RLC Parallel Circuit with Instrumentation

Activate the simulation and record the current readings for both frequencies:

Frequency
Hz

I
S
(RMS), A

I
R
(RMS), A

I
C
(RMS), A

I
L
(RMS), A

550

1000

Table 4 – Current Measurements Simulation Results

Do the current values in Table 4 agree with those obtained in Tables, 2, 3, & 4 of Part A? (Circle your answer)
YES
NO

Remove the DMMs and attach the wattmeter as shown below:

Figure 3 – AC Power Measurement

Record the measurement from the wattmeter.

Frequency

Hz

Source Power, P
S

(
Watts
)

Power Factor

550

1000

Table
5 –
Power Measurement Readings

Do values in the Tables 6 and 2 agree?
(Circle your answer)
YES
NO

If there is any disagreement investigate the source of error and report your findings below:

C. Construct
ion of a Parallel

R, L, C
Circuit
and Measurement of Circuit Characteristics

Construct the circuit in Figure 1.
Set the function generator voltage to 2.5 V RMS and the frequency value to 550 Hz.
Turn the circuit on.
Record the current reading.

I
S
= ______
___
____
(A)
Is this the same as the simulated and calculated value? ___
__
___ (YES or NO)
Measure and record the branch currents:

I
R = ________ (A) I
C = ________(A) I
L = ________(A)
Are the current readings the same as your calculated and simulated values?
(Circle your answer)
YES
NO

If you answered NO, explain why you think they differ.

Repeat Steps 2 through 6 with the frequency generator set to output at 1000 Hz.
I
S
= ______________(A)

I
R = ________ (A) I
C = ________(A) I
L = ________(A)
Are the current readings the same as your calculated and simulated values?
(Circle your answer)
YES
NO

If you answered NO, explain why you think they differ.

IV. TROUBLESHOOTING

Describe any problems encountered and how those problems were solved.

LaboratoryReport Cover Sheet

DeVry University

College of Engineering and Information Sciences

Course Number: ECET210

Professor:

Laboratory
Number: 4
Laboratory
Title:
Analysis of AC Parallel RLC Circuit using Simulation and Construction
Submittal Date:
Click here to enter a date.

Objectives

:

Results:

Conclusions:

Team:

Name
Program
Signature

Name
Program
Signature

Name
Program
Signature

Observations/Measurement

s

:

III. A. 1. RLC Circuit Calculated Impedance and Admittance Values:

Frequency
Hz

Susceptance, Siemens

Inductive, B
L

Capacitive, B
C

550

1000

Frequency
Hz

Total Circuit AC Admittance, Y
T

Complex Notation

Magnitude

Angle

550

1000

Frequency
Hz

Total Circuit AC Impedance, Z
T

Complex Notation

Magnitude

Angle

550

1000

III. A. 2. RLC Circuit Calculated Current Values:

Frequency
Hz

I
R
(RMS). A

I
C
(RMS), A

I
L
(RMS). A

Magnitude
Angle
Magnitude
Angle
Magnitude
Angle
550

1000

Frequency
Hz

{I
R

+ I
C
+ I
L
}= I
S
(RMS), A

I
S
= V * Y
T

Complex Form
Magnitude
Angle
Magnitude
Angle
550

1000

Match? Yes _____ No ______
Explanation:

III A. 3. RLC Circuit Calculated Power Dissipation:

Frequency Hz

P
R
, W

P
S
, W
550

1000

III. B. 3. RLC Circuit Simulation Results:

Frequency
Hz

I
S
(RMS), A

I
R
(RMS), A

I
C
(RMS), A

I
L
(RMS), A

550

1000

III. B. 4. Simulation Values Match Calculated Values:
Match? Yes _____ No ______
III. B. 6. RLC Circuit Simulated Power Measurement:

Frequency

Hz

Source Power, P
S

(
Watts
)

Power Factor

550

1000

III. B. 7. Simulation Values Match Calculated Values:
Match? Yes _____ No ______
Explain any mismatch:

III. C. 4. RLC Circuit Measured Current at 550 Hz:

I
S
= ______
___
____
(A)
III. C. 5. Value Matches Calculated and Simulated Values:
Match? Yes _____ No ______
III. C. 6. RL Circuit Measured Currents:
I
R = ________(A) I
C = ________(A) I
L = ________(A)
Match? Yes _____ No ______
Explain any mismatch:

III. C. 7. RLC Circuit Measured Current at 1000 Hz:

I
S
= ______
___
____
(A)

I
R = ________(A) I
C = ________(A) I
L = ________(A)
Match? Yes _____ No ______
Explain any mismatch:

Questions:

Construct a Phasor Diagram to represent the source current and the branch currents, IR, IC, and IL through the resistor, capacitor, and the inductor. The diagram does not need to be drawn to scale. However, the values of the items represented must be included in the diagram.

Did you notice any interesting feature in the lab exercise with regard to the two different frequencies chosen for the experiment?

In the Multisim simulation, change the frequency of the source to be between 725Hz to 735 Hz (in increments of 2 Hz) and record the inductor and the capacitor currents.

Frequency, Hz

I
R
,

mA

I
C
, mA

I
L
, mA

725

727

729

731

733

735

What do you notice from the readings?

Grade:

Deliverable

Points Available

Points Achieved

Laboratory Cover Sheet
8
Working Circuit(s)/Program(s)
8
Observations/Measurements
6
Questions
8

Total Points

30

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