FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING
Department of Electronics Engineering
3. RLC SERIES RESONANCE
1.
Course, Subject & Experiment Details
Academic Year
2014 – 2015
Course & Semester F.E. (ALL) – Sem. I
Chapter No.
2
Hardware
Experiment Type Performance
2.
Estimated Time Experiment No. 4 – 02 Hours
Basic Electrical and Electronics
Subject Name Engineering Laboratory
Chapter Title
AC Circuit
Subject Code
FEC105
Aim & Objective of Experiment
To study the resonance in RLC series circuit.
To calculate the resonant frequency, bandwidth and Q factor.
3.
Expected Outcome of Experiment
This experiment helps students understand the resonance phenomenon in R-L-C series
circuits. This experiment helps students to draw the resonance curve between current and
frequency and locate the resonant frequency on it. Students are also expected to find out the Q
– factor and Bandwidth of series resonance circuit.
4.
Brief Theoretical Description

A circuit containing R, L and C elements is resonant when the circuit power factor is unity,
i.e. the applied voltage and the circuit current are in phase. If such condition occurs in a
series circuit, it is termed as series resonance.
Basic Electrical and Electronics Laboratory- Experiment 4
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FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING
Department of Electronics Engineering

In an RLC series circuit, when XL = XC, the impedance will be purely resistive in
nature. In polar form impedance can be written as Z 0
= R 0, and the
voltage and current are in-phase. This condition is known as Resonance in R L C
series circuit.
Let f0 be the frequency at resonance.
 At resonance,
XL = XC
2..f0.L =
f0 =

1 .
(2.. f0C)
1
HZ
2.. L.C)
0 =
1
rad/sec.
(L.C)
Impedance of an R L C circuit can be written as,
= R + j (XL - XC)
Z
And magnitude of impedance
Z
=  [R2 + (XL - XC)2]
When XL = XC, the magnitude of impedance will be only R which is the minimum
value possible for Z. At resonance, i.e., at XL = XC , Z will be minimum and hence
current will be maximum. A curve between current as function of frequency is known
as the Resonance curve. The value of current at resonance is denoted by I0. Since I0
is the maximum value of current, the maximum power in the circuit
Pmax
=
I02.R
Half of this maximum power occurs at a current of I0/2.
The corresponding frequencies (f2 and f1) are known as half power frequencies. They
are also known as cut off frequencies.
Band width ,
BW = f2 - f1 = R Hz
2 L
Basic Electrical and Electronics Laboratory- Experiment 4
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FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING
Department of Electronics Engineering
Quality factor
5.
Q = f0
B.W.
Circuit Diagram & Experimental Setup
R
I
L
C
varable freq ac
source
Fig 1
6.
Apparatus and components Required
(a) Apparatus for RLC Series Resonance :Type of
Apparatus
Ammeter
Variable frequency
AC source
CRO
Connecting wires
Symbolic
Notations
A
Specifications
0 - 10 mA M/I
V, F
20 V (p - p)
(b) Components for RLC Series Resonance :Type of
Components
Resister
Inductor
Capacitor
Symbolic
Notations
R
L
C
Basic Electrical and Electronics Laboratory- Experiment 4
Component Values
& Specifications
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FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING
Department of Electronics Engineering
7. .
1.
2.
3.
4.
5.
6.
7.
8.
Experimental Procedure
Connect the circuit as shown in the circuit diagram.
Adjust the voltage to 20 V (p-p).
Keep the frequency to some minimum value (say 10 Hz) and note the current.
Increase the frequency and for each frequency note the corresponding current.
Draw the resonant curve by taking (I) along y-axis and log(f) on x-axis.
Find the resonant frequency, half power frequencies, bandwidth and Q factor.
Compare them with the theoretical values.
Observation Table
Sr. No.
Frequency
(Hz)
Basic Electrical and Electronics Laboratory- Experiment 4
Log(f)
Current (mA)
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FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING
Department of Electronics Engineering
9.
Calculations
Calculation from Graph:
Resonant frequency
Maximum current from graph,
f0
I0
I0
2
f1
f2
BW
Q factor
=
=
=
=
=
=
=
f2 - f1
f0
BW
Theoretical Calculation:
f0
=
1
.
2LC
Maximum current from graph,
I0
=
BW
=
Q factor
=
Basic Electrical and Electronics Laboratory- Experiment 4
V
R
R
2L
1 L
R C
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FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING
Department of Electronics Engineering
10.
11.
12.
Conclusions & Inferences
Practical Applications
Post Lab Questions
1. Write the Effects of series resonance.
2. Draw the phasor diagram for R – L – C series resonant circuit.
3. Derive the relation between Q – factor and Bandwidth of a series resonance circuit.
4. A series RLC circuit has the following parameters values:
R = 10, L = 0.014H, C = 100 F. Compute the following
a) Resonance frequency in rad/sec
b) Q – factor of the circuit
c) Bandwidth
d) Lower and upper frequency of BW
e) Max. value of voltage appearing the capacitor if the voltage v = 1 sin 1000t is applied to
the RLC circuit.
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Basic Electrical and Electronics Laboratory- Experiment 4
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