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CBSE Class 12-science Answered

transformer
Asked by mohitverma1017sn | 30 Dec, 2020, 08:57: PM
Expert Answer
Transformer is a device used to change the peak value of alternating electrical voltage .
If transformer is used to increase the peak value of alternating voltage  it is called step-up transformer and
if it is used to decrese the peak level of alternating voltage it is called step down transformer.  
This stepping up or stepping down is  done using the principle of mutual induction. A transformer consists of two sets of coils,
insulated from each other. They are wound on a soft-iron core, either one on top of the other as in Fig. (a) or on separate limbs
of the core as in Fig. (b). One of the coils called the primary coil has Np turns. The other coil is called the secondary coil;
it has Ns turns. Often the primary coil is the input coil and the secondary coil is the output coil of the transformer.
 
When an alternating voltage is applied to the primary, the resulting current produces an alternating magnetic flux
which links the secondary and induces an EMF in it. The value of this EMF depends on the number of turns in the secondary.
We consider an ideal transformer in which the primary has negligible resistance and all the flux in the core links both primary
and secondary windings.
 
Let φ be the flux in each turn in the core at time t due to current in the primary when a voltage vp is applied to it.
Then the induced EMF or voltage εs, in the secondary with Ns turns is 
 
begin mathsize 14px style epsilon subscript s space equals space minus space N subscript s fraction numerator d ϕ over denominator d t end fraction end style ............................(1)
The alternating flux φ also induces an EMF or voltage εp, called back emf in the primary, which is given as

begin mathsize 14px style epsilon subscript p space equals space minus space N subscript p fraction numerator d ϕ over denominator d t end fraction end style  .............................. (2)
.But εp = vp. If this were not so, the primary current would be infinitesince the primary has zero resistance(as assumed).
If the secondary is an open circuit or the current taken from it is small, then to a good approximation εs = vwhere vs is the
voltage across the secondary. Therefore, Eqs. (1) and(2) can be written as
 
begin mathsize 14px style v subscript s space equals space minus space N subscript s fraction numerator d ϕ over denominator d t end fraction end style.............................(3)
begin mathsize 14px style v subscript p space equals space minus space N subscript p fraction numerator d ϕ over denominator d t end fraction end style...........................(4)
 
From above equations (3) and (4) , we get   ( vs / vp ) = Ns / Np ..................... (5)

Note that the above relation has been obtained using three assumptions:
 
(i) the primary resistance and current are small;
(ii) thesame flux links both the primary and the secondary as very little flux escapes from the core, and
(iii) the secondary current is small.
 
If the transformer is assumed to be 100% efficient (no energy losses), the power input is equal to the power output, 
 
 ipvp = isvs ...........................(6)
 
Combining Eqs. (5) and (6), we have
 
begin mathsize 14px style i subscript p over i subscript s space equals v subscript s over v subscript p space equals N subscript s over N subscript p end style..................(7)
 
If the secondary coil has a greater number of turns than theprimary (Ns > Np), the voltage is stepped up(Vs > Vp).
This type of arrangement is called a step-up transformer. However, in this arrangement,there is less current in the secondary
than in the primary (Np/Ns < 1 and Is< Ip).
 
If the secondary coil has less turns than the primary(Ns < Np), we have a step-down transformer.
 
In this case, Vs < Vp and Is > Ip. That is, the voltage is stepped down, or reduced, and the current is increased.
 
In actual transformers, small energy losses occur due to the following reasons:
(i) Flux Leakage: There is always some flux leakage; that is, not all ofthe flux due to primary passes through the secondary
due to poor design of the core or the air gaps in the core. It can be reduced by winding the primary and secondary coils
one over the other.

(ii) Resistance of the windings: The wire used for the windings has some resistance and so, energy is lost due to heat produced
in the wire. In high current, low voltage windings, these are minimised by using thick wire.
 
(iii) Eddy currents: The alternating magnetic flux induces eddy currents in the iron core and causes heating.
The effect is reduced by having a laminated core.
 
(iv) Hysteresis: The magnetisation of the core is repeatedly reversed by the alternating magnetic field.
The resulting expenditure of energy in the core appears as heat and is kept to a minimum by using a magnetic material
which has a low hysteresis loss.
 
The large scale transmission and distribution of electrical energy over long distances is done with the use of transformers.
The voltage output of the generator is stepped-up (so that current is reduced and consequently, the I2R loss is cut down).
It is then transmitted over long distances to an area sub-station near the consumers. There the voltageis stepped down.
It is further stepped down at distributing sub-stations and utility poles before a power supply of 240 V reaches our homes.
 
Answered by Thiyagarajan K | 31 Dec, 2020, 02:22: PM
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