A

MICRO PROJECT REPORT

ON
“RESONANCE IN SERIES CIRCUIT”
SUBMITTED BY –
Roll No. Enrollment no. Name of student
16 1916440104 Ms. Akshata Suhas Desai
17 1916440106 Mr.Vinayk Shivaji Nikam
18 1916440107 Mr. Lokesh Mukeshkumar Shah

UNDER THE GUIDANCE OF

Mr. P.M.PUJARI

DEPARTMENT OF ELECTRONICS AND

TELECOMUNICATION ENGINEERING SANJAY
GHODAWAT POLYTECHNIC, ATIGRE ACADEMIC
YEAR: 2020-21
 Certificate
This is to certify that the Micro project work entitled
“RESONANCE IN SERIES CIRCUIT”
Has been successfully completed by
Roll No. Enrollment no. Name of student
16 1916440104 Ms. Akshata Suhas Desai
17 1916440106 Mr. Vinayak Shivaji Nikam
18 1916440107 Mr.Lokesh Mukeshkumar Shah

In fulfillment for the

Diploma in Electronics &
Telecommunication Engineering
Maharashtra State Board of Technical Education
During the academic year 2020-21under the guidance of

Mr.P.M.Pujari Mr. R.P.Dhongadi Mr. V. V. Giri

Project Guide H.O.D Principal

DEPARTMENT OF ELECTRONICS AND

TELECOMMUNICATION ENGINEERING
 ACKNOWLEDGEMENT

During the selection of topic entitled as “RESONANCE IN SERIES CIRCUIT” the

help we received from our professors, family, and friends is invaluable and we are forever
indebted to them.
We would first like to express our gratitude to our Principal Prof.V.V.Giri Our HOD
Mr. R.P.Dhongadi our Project Guide Mr.P.M.Pujari for their immense support, suggestion,
encouragement and interest in our micro project work. Without their invaluable suggestions our
project selection would be incomplete.

Roll No. Enrollment no. Name of student

16 1916440104 Ms.Akshata Suhas Desai
17 1916440106 Mr.Vinayak Shivaji Nikam
18 1916440107 Mr.Lokesh Mukeshkumar Shah

Date:-
Place:-Atigre

Academic Year 2020-21

 ABSTRACT:

As a series resonance circuit only functions on resonant frequency, this type of circuit is also known as
an Acceptor Circuit because at resonance, the impedance of the circuit is at its minimum so easily
accepts the current whose frequency is equal to its resonant frequency.
 INDEX
Sr. No. Chapter Name

01 Series Resonance Circuit

02 Series RLC Circuit

Inductive Reactance against Frequency

03
04 Capacitive Reactance against Frequency

05 Series Resonance Frequency

06 Impedance in a Series Resonance Circuit

07 Series RLC Circuit at Resonance

 INTRODUCTION

The mathematical techniques will use simple properties of complex numbers which have real
and imaginary parts. This will allow you to avoid solving differential equations resulting from
the Kirchoff loop rule and instead you will be able to solve problems using a generalized Ohm's
law. This is a significant improvement since Ohm's law is an algebraic equation which is much
easier to solve than differential equation. Also we will find a new phenomenon called
"resonance" in the series RLC circuit.
Series Resonance Circuit

Resonance occurs in a series circuit when the supply frequency causes the voltages across L and C to
be equal and opposite in phase. Thus far we have analysed the behaviour of a series RLC circuit whose
source voltage is a fixed frequency steady state sinusoidal supply. We have also seen in our tutorial
about series RLC circuits that two or more sinusoidal signals can be combined using phasors providing
that they have the same frequency supply. But what would happen to the characteristics of the circuit
if a supply voltage of fixed amplitude but of different frequencies was applied to the circuit. Also what
would the circuits “frequency response” behaviour be upon the two reactive components due to this
varying frequency. In a series RLC circuit there becomes a frequency point were the inductive
reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor. In other
words, XL = XC. The point at which this occurs is called the Resonant Frequency point, ( ƒr ) of the
circuit, and as we are analysing a series RLC circuit this resonance frequency produces a Series
Resonance.

Series Resonance circuits are one of the most important circuits used electrical and electronic circuits.
They can be found in various forms such as in AC mains filters, noise filters and also in radio and
television tuning circuits producing a very selective tuning circuit for the receiving of the different
frequency channels. Consider the simple series RLC circuit below.
Series RLC Circuit

Firstly, let us define what we already know about series RLC circuits.

From the above equation for inductive reactance, if either the Frequency or

the Inductance is increased the overall inductive reactance value of the inductor
would also increase. As the frequency approaches infinity the inductors
reactance would also increase towards infinity with the circuit element acting
like an open circuit.
However, as the frequency approaches zero or DC, the inductors reactance
would decrease to zero, causing the opposite effect acting like a short circuit.
This means then that inductive reactance is “Proportional” to frequency and is
small at low frequencies and high at higher frequencies and this demonstrated
in the following curve.
Inductive Reactance against Frequency

The graph of inductive reactance against frequency is a straight line linear

curve. The inductive reactance value of an inductor increases linearly as the
frequency across it increases. Therefore, inductive reactance is positive and is
directly proportional to frequency ( XL ∝ ƒ )
The same is also true for the capacitive reactance formula above but in reverse.
If either the Frequency or the Capacitance is increased the overall capacitive
reactance would decrease. As the frequency approaches infinity the capacitors
reactance would reduce to practically zero causing the circuit element to act like
a perfect conductor of 0Ω.
But as the frequency approaches zero or DC level, the capacitors reactance
would rapidly increase up to infinity causing it to act like a very large resistance,
becoming more like an open circuit condition. This means then that capacitive
reactance is “Inversely proportional” to frequency for any given value of
capacitance and this shown below
Capacitive Reactance
against Frequency

The graph of capacitive reactance against frequency is a hyperbolic curve. The

Reactance value of a capacitor has a very high value at low frequencies but
quickly decreases as the frequency across it increases. Therefore, capacitive
reactance is negative and is inversely proportional to frequency ( XC ∝ ƒ -1 )
We can see that the values of these resistances depends upon the frequency of
the supply. At a higher frequency XL is high and at a low frequency XC is high.
Then there must be a frequency point were the value of XL is the same as the
value of XC and there is. If we now place the curve for inductive reactance on
top of the curve for capacitive reactance so that both curves are on the same
axes, the point of intersection will give us the series resonance frequency point,
( ƒr or ωr ) as shown below.
Series Resonance
Frequency

where: ƒr is in Hertz, L is in
Henries and C is in Farads.
Electrical resonance occurs
in an AC circuit when the two
reactances which are
opposite and equal cancel
each other out as XL = XC and
the point on the graph at which
this happens is were the two
reactance curves cross each other. In a series resonant circuit, the resonant
frequency, ƒr point can be calculated as follows.
We can see then that at
resonance, the two
reactances cancel each
other out thereby making
a series LC combination
act as a short circuit
with the only opposition
to current flow in a series
resonance circuit being
the resistance, R.
In complex form, the resonant frequency is the frequency at which the total
impedance of a series RLC circuit becomes purely “real”, that is no imaginary
impedance’s exist. This is because at resonance they are cancelled out. So the
total impedance of the series circuit becomes just the value of the resistance
and therefore:  Z = R.

Impedance in a Series Resonance Circuit

Note that when the capacitive reactance dominates the circuit the impedance
curve has a hyperbolic shape to itself, but when the inductive reactance
dominates the circuit the curve is non-symmetrical due to the linear response
of XL.
You may also note that if the circuits impedance is at its minimum at resonance
then consequently, the circuits admittance must be at its maximum and one of
the

characteristics of a series resonance circuit is that admittance is very high. But

this can be a bad thing because a very low value of resistance at resonance
means that the resulting current flowing through the circuit may be dangerously
high.
We recall from the previous tutorial about series RLC circuits that the voltage
across a series combination is the phasor sum of VR, VL and VC. Then if at
resonance the two reactances are equal and cancelling, the two voltages
representing VL and VC must also be opposite and equal in value thereby
cancelling each other out because with pure components the phasor voltages
are drawn at +90o and -90o respectively.
Then in a series resonance circuit as VL = -VC the resulting reactive voltages are
zero and all the supply voltage is dropped across the resistor.
Therefore, VR = Vsupply and it is for this reason that series resonance circuits
are known as voltage resonance circuits, (as opposed to parallel resonance
circuits which are current resonance circuits).

Series RLC Circuit at Resonance

Since the current flowing through a series resonance circuit is the product of
voltage divided by impedance, at resonance the impedance, Z is at its minimum
value, ( =R ). Therefore, the circuit current at this frequency will be at its
maximum value of V/R as shown below.