Electrical Resonance

The Tesoqnce is Commorn

systems phenome
that
that have tenleney to oslote
Osc lode
amea
the natwnal
equh
This teguenyi Callo
Osei llati&n ot Sysem.
I* such a system us diven by cm enena
Sowce ahose ueney ds egua o the netural
regueney ot the systen then the ompituole o7
Oscilatio be comes large amd resnance
resnane s sold to

Seies Resonance Cireit

-A clreit in ohich indutane .L, Capacitane
C and reaistance R
the cirçit admits ae cormeted in seriés, amol
maximum crent Correspnding
to a Aven trqeny o a.c., w calleo 3eies

L R

At+ vey lous teguancies, induchve eactame XL = oL

is negl ble bt'capatve reactane
is vey igh Xe e 1/we
As the
to the circut is'nere,XL e
lteinating emf alied
amd xe goes on decreoding goes bn increasing
For a parieula value ot w
(Say wr)

JLC
 A

JLC 2nfy
So
211 J LC
XL Xe So
At this particula troeny tr as

= R C minimum)
RLC rcit s minimum
So Hee impedance oj RLC
amd hene the cwsunt I, = E - REe becomes
makimum.
This trequeny s call seies resonance foequent
Io
R=102

R Decreases
Q Increases

R= 100

The vaiation ot circut peak cuent with

theichangingy epslie votoge
shoun
(I) It s de that for enies
or s than wr th yalues
less than the maeimum value
(H) at peok wet
manimum (I, ). 21
 Q" Factor ot Resonanie Circut
a sees resonat
The characteistic
duteminedl byo,factor Quality
4he a facto or Qua
tator ot the cdreut at resnane
It dutnes shapns ot tuning
resonat cireut
o a seiesvoltoge
The Q- factoy developeol
s detineo as the Yatio
ratio copactance at resonane
acYos the inductance bhich Us the voltoe
to the impresses voltoge
applie acroce R.
Voltoge across L o e

alied Voltogel=Voltage acrass R)

(wyL)I WrL
RI RC Or
RI R

sing waing Wr

RC

* As R is mcreoseo factor ok the circut

decreases.
The vales o q wsually vuy foom lo to Loo.
The electonic cieits with high a values
woutd Yesp resnane'
veuy narow range o teanci
anel shape is th

25
Q ) Inna seies L-c-R icuit, the voltages acos an
inductor, a copacitor amal a resistor e 3ov,
Sov and Gov tespectively whot is tha phave
ditteence betuweh the applie voltage and the
Cwvuntn th rewt ?
Sol. Given that VL= 30V, Ve =3ov, Va 6oV
can See that VLe Vc Hence thhe circwt
Here we
is in esonanee,so Hhere will be no phase olierene
between the appliecl voltoge ond Cweent
A radlo can tme oves the tregenykHzTange
o
os a pOtion ok Mw breaclcast bamd(8o
200 KHe). ; ts Le cut has an
then ohot must b
H, the
induetance,its
o 20p
vajable Capaitor ?
romge
Given that
8oD K Hz BXIoH2

5J
L:
1200 K H
20D

CapacityH Tomge batween Ci amd Ca

H
l2x10
200 XIO6 H
Hz

From
27TLC
So
C z
u Lf
C 197.7 xb2 F
F 197.7 PE

Sinsilay , Ca

Ca
C2 87.8.PF
RG
Average Pouwer in RLc cineit
Lt the atelm ating emf. appiec to
E E. Sinwt
behinc
altenating cuant deeloped Lags
It ,then -
aÞpie enf. by a phoae ongHe
the applied
I Io Sin l w t )
Pouoes at instomt t , d

So Eo Simwt * Io Sin (wt - )

Coswt Sino)
Eo Io Sin tot (sinwt Cosc
Sinwt Coot Sm
Eo I, Sinot Cas - Eo Lo
: Eole Sinwt Ces - E I sin 2wt Sin
2
peues is ousumed to emain
It this inatantaeous nme t then Smo amount
Constamt tor a Smol ti
wok aorie in this time is
of
(E. I. Snot cos - gesm2t Sin ) t
Tötal work done oves a Comlete cycle s
fEI, sitst Cosþ dt - fe, sin 2ot Sind d
Es I, Cos Sii ot dt - Ele sin fsm2t dt
2
T
As Sinwtdt = ond f sint ot =o

Avege poe in the RLe Crcit over a

Cemelee ele
P =
 So
EvIo Cos

P = Cos
P Ems Ims Cos
a Complete
over protu cycle in
Hene average power ct
inducttve C t the,
the produt"otm s emf.
Omdl r.ms. amd cosine ot th phoe mge
betueen the votage nd cwrent.
¢ Tha aboe relaion u abpicoble to a l ac.
circuits.
Cos nd z will have abpropriate values tor
d i t e t cireits.
æ)Only R cire uit
Cos = 1
(i1) Only L cire it
XL amd Cus = 0
(tii) Only c cire it -
amd Cas
Cv ) In RLe Circuit
N

(v) In RL cive uit -

N
Cos

() In Re cireit
amd Ces
(i) In Le icit
Q, amd = 90
Power Factor of an A.C. Circuit
We Kno hat te aveage pBwer in RLC CYcut
ven by -
P= Ems Immg Cos
Here P is calle true powe, (Ems Ims) s calld
apparent
Caleo
powe oY virtued power and Cos
power tactoy ot the' ircit

Power Fator( Cos¢)= True Power (P)

p p a e t Pooer

From diagram- Ve
Cos = Eo
V
IR
Iz

Pooawer factor = Cos = R

In a non - nductive crc it,
Power factor = Cos - 1
Tis the naximum value ot power tactor.
(i) In a Pue inouctoy o an idleal capaitor
90
Power Fato Cos
So avege Powe consueal in a pPwe inoduetor
Laleal capator
P = Em Im Coso o
In aetual pra ctice we co nat have ideal
mductoY ideal capaitor - Therejpe, theAe loes Occ
Some issipation ot enh
a l Am inductor and a, bulb ae Connecte in series
Sto an AC Sown . 12V, SD He, 2A Cwunt Hows
the dreit ne he phase anle between vote
Cunent is s/4 rad. C
Calcuate
i a t e the impedane
impeane
Hhe ircut.
omd inductanCe of the
Sol: Given hat Vms l2V
/4 Iyms 2A
Imped anca
Irms
Aso, powe fator Cos = N

R
R 6Cosi
In L-R cireuit R?+ X
So

XL - s - 6a) 3 J2
But XL = 2J1fL
3J2
2x3.IsXSo

A Capattor and resiator ae Conneete

CASE
in Seies with an Ae Sowce. I; the potential
c, R ane 120v, 9ov rapectvey
2016

difvunce
and the
ms cwwent ot the cire uit ia 3A,
Caleulate the HancR,
ok
b) Posen faetor .

Sol Griven that- Ve 12ov , Va 9o,

suies Ac rcuit
Vrms

Yns =(20) +(90)

Lrms Vms. Vrns
Tms
 Irms Vims.
2
Vrms
Ims

(b) Ve R

R B0
Power factoy (Cos ¢) :
Power factoy e

CHOKE COL
Choke coil is simply a coil having alarge
inductance but a small esistance.
Copper kwire

Conshnucion- Choke Coil is made

by a thick Copper wire to reduce
ts resistance . It is wounded on
a plated Sott iron Core o increse Seyt iron
Core
ts sl% inductance.

Pinciple -
At most places , the househad eleetic power is
Supplieo at 220 V, so Hz 7 such a sowce is irectly
Connected to a merewy tube, the tube will be damaged.
To reduce the curent, a choke Coil is Conecte
in seies with the tube.
Power Consumeo in an AC. circut ds P Erms ImCos
for pwu inductor
So that
Hene the qdvm tage o using choke Coil to reouce he
voltaqe s that an inductoy does not consume power.
Henea we do not ose electric engy in he torm o7 heat
Wattless Current or Idle Current
The cwent cohich Conumes no Power tr its
maintenance in the cireçt is calld at less cwent.
we Knoo that ayerage power oves a complete
inductive circwt
yoe in an
P Ems Irms Cos¢
Tm a pautewlan cireit, Suppose Ems deods Ims
bg phas mgle , as shown in tgue.
Eyms

OTrms Sing Irms X

Irms Com be resolved into two rectagwas Conponents

As phoe omge betueen Ems and Ims Coso 's Zero.
.

average pouwe Cosumed p

due to 'Component Lims Cos
cyde in the cieit
ce
Pav ms( Ims Cos) Cos o Ems Ins Cos
Again as phase angle between Erms d Irms Sin
a T/2 So avehage pbwe Corsumed per eyce in the
circut due to component Irms Sin is -

- Ems (Iny Sin)CosT

The Com ponent Ims Sin makes n0 Cortbution to
the consumption o poue in the ae. ireiit.
That is shy this Conponent Lms Sin us Calld the
idlle componer oY wodtHeis Component o% ae. an the.
Component Imy Cos às Callc wodtibull co mponent o% aic.
 À.C. GenerodoY
or A.C. Dynamo
An ac. generator/ dynano
dynamo is
is a machine which
Prouces ltenaing Cwan energy tron mmehanica
'enena
It i mOst impottant abplicadins ot the phenonenon
O electomagnetie induction. The as desigmed
nerator was
oiginally by a Yugoslav scient& t Nikola Testa?
Principle - An
aC. geneAator /dynamo is base n he
indychon whenever the
phenomena os electorhegrn:y a coil change
Gnount o maute,
an em:f i iñdued 'in the Coil.
TRe ess ertial pots ot an aC genenator
(i) Armature - a rectangulos motwe cohl.
ABCD a

It consist ot aa lasge numbes os twns ot insulated

wire wound° ove a Lamnatel Co
sott iron Core.
Copper utoteo about the Cental ais.
The C¡il Can be

Gi) Field Manets

N amd s ae the pole pieces o*
a
Shong electomagnet in wich the imatihe coil s
Yototec? Axis
4 ot votation perpondiculas o the
magretie fiekt hes. 37
Cià) sip Rings
Kj md R ae tuo hollow metalic
ings, to hich two endls ot ahmatwe coil ae
Connectel.
os the coil. Thse vings rotate witt the rot otion
(iv) Brushs -
B) onnd B e tuo Hei ble
meal Pe OYC n ods Thuy e ixec omd
Carbon
ae Kept in igt Contat with ama 'R respechvel
The puepose o kbrushes s to paus on Cunt on
the amoue coil to the extenal Load reaistance R.
working
As the matue col às votated in the magnet
ted, amge e between the tield ard normal to the
Eoil chatges Contmuously. Thereore magnete Hux inkudl
with the cil changes. A onn e'mf. is induud in the
Coil.
To stat with, suppose the Coil is perpendicuk
to the plan ot the paper in whlch magntc ild is
abpied'; with AB at ont amd co at he back.
The arnot ot tux dinkec with Coil in this position t
maximum.
As the col is rotateo amticdckwise, AB nDVE
moved
mwaes omd ves outwads The amounct o
cD noves
magntie tux linked with the Coil Charges.
According to Fleming's ight hamd rue, Cusert
induced
om
om c to D. In the entena circit, cwtrt ows
Ate hals the rotation ok the coil, AG is at
the back amd cD S at the hront (Hgune(b)). 7hereore
mores
m rotating twthr, A moves outwarts ond
jnwauds.
The cshent inducec n aDThrough
is tom s to A, omd
extenal cireut,
Cwent lows tron ) to Bz.
 Inuec Cusen in the extehna cireut changes
rotation ot h
the coil . Heñce
direction
the
c

cuent
t mduced in coil is attetnating
u k has ,

in natwe

Magntude ot induced emf.

magnetie tux nked wih the cot L
= NA Cos

NBA Cosot

whre wiAangulaa velocity os the

coil.
As th Coil rotatd , changes ,s theratoe
ond
magnte
hhce
ehangs
the coilcoil.
inkal with in
flux the
an emf. s inducec jndued in
At this instant t . 4 e is the em.f.
thhe ceil , t h n
- (BA Cosot)

-NBA (Cosot) = -NAA (-sinwtb) a

e NGAw Sinot
OY

will be maximum when

The induceo em.f.
Sin ot = maxinym

by equatin we gut
e, Sinwt

I Sinwt

I Sinwt
Transformer
A transfmer is an electical dlca ch s
wed tor chging the ac. voltoges.
A transtormes which inereases the a.c. voltages
amd a transtormer chieh
skp up
iu Caled step up voltogbs
transtome
s Called a step doon tenstor.
decreases the a.c.

Priniple - transtome s baseo om the principle

A A
mutua induction i-e. henewer the qrnount o7 magree
Alx inkacd with a coil
Coil changes an em.f. is induledl
in the neighbouing
Construction - A transtomer Consist ot aSobt
iron core masle ot Laminate shets, well nsuatec
m egch othet.
Two oils Coil) cmd SS
(Secondly Co) ane ound n the same Core but
ae wel nslated t m each othe. Note that both
trn the Core.
the cls ae also biswlated
The sowe o tenoting emf. L to be
transtormed)) iss connete is toCemnected
the primary coil P
prtma
to he secorry
qmd a load resistane R
Coil S,S.

P
N
INPUT
P
Ac. RS OUTPUT

AMINATED CORE
Woking
Let the ateting e-mf. splied by the
Q.c. Sowce Conneeted to pimart
Ep E, Sin)t
E. 40
 he atenaing.
magnetic Hux a pAimay Cuent induas an astematirg
rh Core. Beca use the core
exfends hrou the twn ok setoncany so the
inelue Hun ux also extends th'ugh the' seeony
winoling
induction th to thee.m.f.Faraday's Law o elettrngnehc
induud per'tun (Em) is Sarne
for both paimany 4 secondany inding
Exnn Np Ns
Hee p, ns repesents the tota numbes ot t n s
in the pimany omd secondany oils Aespectivey.
Ns
Np
As e assume that no enengy i Jast alona
the way Consewation o eneg Tequives that.
Lnput Powes Owtput Power
Ip Ep : I,Es
Ep
In geneal Es. Ns K
Ep Np

Hee
K =trmsfrmativn ratio
Note -
Ns > Np then Es > Ep then the tronstumr
step up hrenstpne
Ng < Np then Es < Ep then the transmur
is called a step down toemsona.

41
 Efciency of transformer
It is ditined as the ratio ot owtput powe to
the inpt power
Output Pouer
Xlo0
Input Powe

Ep Ip
Note -
The trans7ormer Cannot urork on de Atranssorner
choges ac. velfoges /cwsunts It does mot ateche
krequency o7 a.c. ohen a.C. voltege is rased n times,
the Coresponding altarating Curent reduces to /n tmes.

Energy Losses in a trana former

() Copper Loss
It is the eneay as in the tprnm
%heat in the Coppes coils o# a ontormer. Thi s
cau to Joule heating o7 Comduching wites. These ae
minimised wang thick wire
(Gi)Iron Loss -
It i the enesqy. das in the trm
o7 heat mthe ion Core Db thetanstormer This is
oue to tormation o~ eody. cutnts in iron Core. Tt is
mmimised by takina Laminated Corea.
42
(ii) Leakage o magnetie fyx
Dw to thid
this the rade ot chane ot mognti
tux linked with rou oö"ess
each tusn
the rate
ata ot by hom
winding
egch
change ot magnehc ttux inkecd aith
he
pimay nd secomay Coils oves
ne oves he othe

(w) Hysteresis Loss This is the oss ot eneay

due tto repeated maratisation amd lemmosnetisason
O the i n Core when ac. is ted to t The loss
is Kep to a minimum a magnetie matsa
which has aa doo hystensis
(v) Magnetostriction- It is humming noise %a
totormey. Thretrt, output pouwer im the bat
transtsmeA. may be voghy 90% ot the input pout.

PUSH
YOURSELP
BECAUSE ND
ONE ELSE IS
GOING TO DO
0T FOR YOU 43