Transformer based on the Principle of mutual induction according to this
principle, the amount of magnetic flux linked with a coil changing, an e.m.f
is induced in the neighbouring coil.
transformer consists of a rectangular shaft iron core made of laminated
sheets, well insulated from one another. Two coils p1 & p2
and s1 & s2 are wound on the same core, but are well
insulated with each other. Note that the both the coils are insulated from
the core, the source of alternating e.m.f is connected to p1p2,
the primary coil and a load resistance R is connected to s1 s2,
the secondary coil through an open switch S. thus there can be no current
through the sec. coil so long as the switch is open.
ideal transformer, we assume that the resistance of the primary & secondary
winding is negligible. Further, the energy loses due to magnetic the iron
core is also negligible.
INTRODUCTION OF TRANSFORMER
A transformer is an electrical device which is used for
changing the A.C. voltages. A transformer is most widely used device in both
low and high current circuit. As such transformers are built in an amazing
strength of sizes. In electronic, measurement and control circuits,
transformer size may be so small that it weight only a few tens of grams
where as in high voltage power circuits, it may weight hundred of tones.
In a transformer, the electrical energy transfer from one
circuit to another circuit takes place without the use of moving parts.
A transformer which increases the voltages is called a
step-up transformer. A transformer which decreases the A.C. voltages is
called a step-down transformer.
Transformer is, therefore, an essential piece of apparatus
both for high and low current circuits.
THEORY AND WORKING OF TRANSFORMER
When an altering e.m.f. is supplied to the primary coil p1p2,
an alternating current starts falling in it. The altering current in the
primary produces a changing magnetic flux, which induces altering voltage in
the primary as well as in the secondary. In a good-transformer, whole of the
magnetic flux linked with primary is also linked with the secondary, then
the induced e.m.f. induced in each turn of the secondary is equal to that
induced in each turn of the primary. Thus if Ep and Es
be the instantaneous values of the e.m.f.’s induced in the primary and the
secondary and Np and Ns are the no. of turns of the
primary secondary coils of the transformer and
Dфь / dt = rate of change of
flux in each turnoff the coil at this instant, we have
Ep = -Np dфь/dt
Es = -Ns dфь/dt
the above relations are true at every instant, so by dividing 2 by 1, we get
Es / Ep = - Ns
is the instantaneous value of back e.m.f induced in the primary coil p1,
so the instantaneous current in primary coil is due to the difference (E – Ep
) in the instantaneous values of the applied and back e.m.f. further if Rp
is the resistance o, p1p2 coil, then the
instantaneous current Ip in the primary coil is given by
= E – Ep / Rp
E – Ep = Ip Rp
resistance of the primary is small, Rp Ip can be
neglected so therefore
E – Ep = 0 or Ep
back e.m.f = input e.m.f
equation 3 can be written as
Es / Ep = Es / E
= output e.m.f / input e.m.f = Ns / Np = K
is constant, called turn or transformation ratio.
step up transformer
Es > E so K > 1, hence Ns
step down transformer
Es < E so K < 1, hence Ns
If Ip = value of primary current at the
same instant t
And Is = value of sec. current at this
Input power at the instant t
= Ep Ip and
Output power at the same instant = Es
are no losses of power in the transformer, then
Input power = output power Or
= Es Is Or
Es / Ep
= Ip / Is = K
step up transformer
As k > 1, so Ip > Is or
Is < Ip
current in sec. is weaker when secondary voltage is higher.
whatever we gain in voltage, we lose in current in the same ratio.
Similarly it can be shown, that in a step down transformer, whatever we lose
in voltage, we gain in current in the same ratio.
step up transformer in reality steps down the current & a step down
transformer steps up the current.
Efficiency of a transformer is defined as the ratio of output power to the
input power. i.e.
η = output power / input power = Es
Is / Ep Ip
an ideal transformer, where there is no power losses, η = 1. But in actual
practice, there are many power losses, therefore the efficiency of
transformer is less than one.
Following are the major sources of energy loss in a transformer:
Copper loss is the energy loss in the form of heat in the copper coils
of a transformer. This is due to joule heating of conducting wires.
Iron loss is the energy loss in the form of heat in the iron core of the
transformer. This is due to formation of eddy currents in iron core. It is
minimized by taking laminated cores.
Leakage of magnetic flux occurs inspite of best insulations. Therefore,
rate of change of magnetic flux linked with each turn of S1S2
is less than the rate of change of magnetic flux linked with each turn of P1P2.
Hysteretic loss is the loss of energy due to repeated magnetization and
demagnetization of the iron core when A.C. is fed to it.
5. Magneto striation
i.e. humming noise of a transformer.
A transformer is
used in almost all a.c. operations
In voltage regulator for T.V., refrigerator, computer, air
In the induction furnaces.
A step down transformer is used for welding purposes.
A step down transformer is used for obtaining large current.
A step up transformer is used for the production of X-Rays and
Transformers are used in voltage regulators and stabilized
Transformers are used in the transmissions of a.c. over long
Small transformers are used in Radio sets, telephones, loud
speakers and electric bells etc.