is phenomenon is known as self induction and the
emf induced is known as self induced emf or back emf.
When a current I ows through a coil and φ is the
magnetic ux linked with the coil, then
φ v I or φ = LI
where L is coecient of self induction or self inductance
of the coil.
e self induced emf is εφ
=−=−d
dtL
dI
dt
Self inductance of a solenoid is L = P 0 n^2 lA
where l is length of the coil solenoid, n is number of
turns per unit length of a solenoid and A is area of cross
section of the solenoid.
Self inductance of a circular coil is L
NR
=
μπ 0 2
2
where R is the radius of a coil and N is the number of
turns.Mutual Inductance
Whenever the current passing through a coil or circuit
changes, the magnetic ux linked with a neighbouring
coil or circuit will also change. Hence an emf will be
induced in the neighbouring coil or circuit. is
phenomenon is known as mutual induction. e coil
or circuit in which the current changes is known as
primary, while the other in which emf is set up is known
as secondary.
Let IP be the current owing through primary coil at
any instant. If φS is the ux linked with secondary coil
then φS v IP or φS = MIP
where M is coecient of mutual inductance of two coils.
e emf induced in the secondary coil is given by
εS M P
dI
dt=−
Combination of Inductances
When two coils having self inductance L 1 and L 2 are
connected in series keeping them far apart (so that
mutual inductance between them is negligible), the
equivalent inductance of the combination is given by
L = L 1 + L 2
When two coils are connected in parallel, the equivalent
inductance is given by
111
LL 12 L
=+
Energy Stored by an Inductor
A current-carrying inductor stores energy in the
magnetic eld associated with it and energy stored for
current I and an inductance L are related as^1
2
LI^2.
AC GENERATOR
It is a device used to obtain a supply of alternating
emf by converting rotational mechanical energy into
electrical energy. It is based on the phenomenon of
electromagnetic induction. i.e. when a coil is rotated in
uniform magnetic eld, an induced emf is produced in
it.
e instantaneous value of the e.m.f. produced is given
by H = NBAZsinZt, where N is number of turns of the
coil, A is the area of coil and Z is angular frequency of
rotation of the coil in a magnetic eld strength B.Basic Principle of AC Generation
Alternating voltage is generated by rotating a coil
of conducting wire in a strong magnetic eld. e
magnetic ux linked with the coil changes with time
and an alternating emf is thus induced. Instantaneous
ux linked with coil is
φ=()⋅
ABn
= ABn cos(Zt + q 0 )
where,
A = area of the coil (in m^2 )
B = magnetic eld (in tesla)
n = number of turns
ωπ
==angular frequencyi= πν n rad s−2
2 1
T
()
Q = frequency (in hertz)
q 0 = initial phase angle.
and the alternating voltage is given byVd
dt=− =Vtφ
0 sinωWhere V 0 = ABnZ
e instantaneous value of an ac is given by
I = I 0 sin Zt
Here, Z is the angular frequency of ac and (Z/2p) is the
frequency of ac. (2p/Z) represents the time period of ac.
In one cycle of ac, current increases from zero to a
maximum, then decreases to zero and reverses in
direction and then decreases to zero. us current is
zero twice in one cycle and is numerically maximum
also twice in one cycle, once in the forward direction
and once in the backward direction in one cycle. Time
taken to complete one cycle is called Time Period.
e frequency of ac represents the number of cycles of
ac completed in one second. Ac supplied in India has a
frequency of 50 Hz.wB
qw= t
n