ELECTRO

MAGNETIC
INDUCTION
 Faraday Henry

1791 -1867
1867 1797 –1878
1878
Laws:-
Faraday’s Laws :-
1) When ever there is a
change in magnetic
flux linked with a
coil a current is
coil,
generated in the coil.
The current is called
induced current and
the emf responsible
for the current is
called induced emf
emf.
The phenomenon is
called
ll d electro
l t
magnetic induction.
2) The induced emf
(t e induced
(the duced
current) is directly
proportional to the
rate of change of
magnetic flux
flux.
(The emphasis is
on the change of
flux))
Lenz’s Law:-
The direction of the
induced current
(induced emf) is
alwaysy to oppose
pp
the cause for which
it is due. (Emphasis
is on cause)
Motional emf,
emf Self
induction,mutual
induction and Eddy
currents.
Motional emf = BLv volt.
self inductance of a coil
is L = µ0 µr N2 A
(µr is the relative
permeability of the core),
µr = 1for air core
Mutual- induction: Between Pair
of coils
coils, M = µ0 µr N1 N2 A henr
henry
(µr is the relative permeability of
the core µr= 1, for air core.))
Eddy currents :-
They are cyclic currents also
called focault current in the
b lk off a metall in
bulk i a direction
di i
perpendicular
p p to the magnetic
g
flux. They cause heating effect
and dissipate energy
energy. This can be
minimized by using laminated plates.
 Alternating
g current
(Alternating voltage)
The current which oscillates
between a positive
maximum value and
a negative minimum
value is called alternating
c rrent(ac) The emf responsible
current(ac).The
is called alternating voltage.
V = V0 sinωt is the
expression for
alt
l - voltage
l
I = I0 sinωt is the
expression for
alt - current0
e0 and i0 are the peak (max) values
of the induced voltage and
induced current respectively.
ωt = sin-1 V/ V0 or ωt = sin-1 I/ I0 is
called
ll d the
th phase.
h If ωtt iis the
th same
for current and voltage, then they
are said to be in phase.
 Vave = ( 2/π)V0, I ave = ( 2/π)I0
Vrms = V0, /√2 I rms = I0 /√2

P rms = V rms I rms

P rms = (V0, /√2 ) X (I0 /√2) = V0 I0 /2

is called half power point in ac circuits

 AC applied to resistance,
resistance ideal
inductance and ideal capacitance.
Ideal means inherent resistance of the
circuit component is not considered
for discussion. Power in AC
circuits:-
i it Pac = V I cosφ. V=
V PD
measured. I= Current measured ,
φ is the phase difference between
voltage and current .
 φ is called the p
cosφ power
factor in AC circuits because
the magnitude of power
transfer in AC circuits is
di t t d by
dictated b cosφ .
 pp
AC applied to resistance

Th behavior
The b h i off resistance
i is
i
identical for both AC and DC (we
know that Pdc = Voltage x current)
The value of resistance is
independent of frequency.
The voltage and current are
always
l in
i phase
h in
i a resistance.
i t
That means, in a purely resistive
AC circuit ,ie., φ = 0,
cos φ = 1 . Pac = V I watt
watt. In other
words For a resistance Pdc = Pac
The behavior of inductance for
DC is transient where as for
AC it is perpetual. It offers
Inductive reactance
XL = ωL = 2πfL ohm to
AC. XLα f, the frequency of the
Applied AC.
The applied voltage and the
resulting current through
the pure inductance are not
In phase V = V0 sin ωt.
I = I0 sin (ωt - 90 ), φ = 900
The current lags behind the voltage
by 90 .
Pac = V I cos φ = Pac = V I cos 90
Pac = 0 watt
The AC through
g an ideal inductance
is called Watt less current.
AC applied
The behaviorto
ofacapacitance
ideal capacitance
to DC is
instantaneous where it gets charged
to the potential of applied DC voltage.
voltage
When Alternating
g voltage
g is applied
pp
across ‘C’ its action becomes perpetual.
It offers a capacitive reactance.
Xc = 1/ωC = (1/2πf C) ohm.
ie, Xc α 1/f V = V0 sin ωt
I = I0 sin
i (ωt
( t + 90)
The applied voltage and the
g current are not in phase.
resulting p
The current leads the voltage by 90 .
 Series RLC circuit
Here a resistance, an ideal
inductance and an ideal capacitance
are connected in series with a plug
p g
key. When the key is closed the
source drives a current through the
series combination and maintains an
effective voltage V across the
combination.
The effective voltage can be
obtained by a vector (phasor)
diagram. V = √{V2R + (VL- VC ) 2}
V = I √{R
√ 2+ (XL- XC ) 2},
V / I = Z ohm called the
Impedance ( Effective resistance
offered
ff d tto AC by
b the
th series
i RLC
circuit). Z = √{R2 + (XL- XC ) 2} ohm
 Series resonant circuit
A series RLC circuit connected to
an AC source of adjustable
frequency (function generator) is
called a series resonant circuit.
When the circuit is switched on, it
drives a current through
g the circuit.
The magnitude of the current
depends on the impedance Z. Z
But impedance depends on the
values of R, XL and, XC..
R is independent of frequency,
XLα f and XC α 1/f.
Z = √{R
√ 2 + (XL- XC ) 2} ohm.
At low frequencies of the applied
AC (XC > > XL), √ (XL- XC )2 is very
l
large , ‘ Z’ is
i large
l and
d ‘I’ is
i small
ll
At high frequencies of the applied
AC (XL > > XC), √ (XL- XC )2 is again
very large, Z is large ‘I’ is small .
Therefore When frequency increases
from a low value to a high value XC
decreases, XL increases. At one
particular frequency fr , XL = XC,
C
Z = Zmin = R. I increases gradually
And becomes maximum I = I max at fr .
This point of I = I max is called
electrical
l t i l Resonance
R and
d that
th t
particular frequency is called
resonant frequency
q y fr .
 Resonant frequency.
At fr , XL = XC, Z = R, Power factor
Cosφ = R / Z
2π fr L = 1/2π fr C fr = 1/2π√(L C)
Q factor :-
Q = (Voltage across L)/(Voltage across R)
at resonance.
Q = (VL / VR ) = IXL /IR = XL /R
Q = 2π fr L/R But 2π fr = 1/ √(L C)
Q = (L/R) x (1/ √(L C) = [√(L/ C)] x 1/R
•
At half power frequency
I = (Imax /√2). Band width = f2 - f1 and
Q = fr /(f2- f1).
) Q value
l iis also
l called
ll d
the sharpness of resonance or
y of the resonance circuit.
selectivity
Q is large when R is small.
(1) (2)
 Transformer

For an ideal transformer

transformer,

(V / V ) = (N / N ) = K

K is called Transformer turn ratio

ratio.
K> 1 N > N it is called step
up voltage transformer.
K< 1 N < N it is called step
down voltageg transformer.
K = 1 N = N it is called
buffer transformer (Used in circuit
isolation and impedance matching).
Input power = out put power
V I =V I