. T RANSFORMERS For many purposes, it is necessary to change (or transform) an alternating voltage from one to another of greater or smaller value. This is done with a device called transformer 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 N p turns. The other coil is called the secondary coil ; it has N s 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 v p is applied to it.
Then the induced emf or voltage ε s , in the secondary with N s turns is s s N φ = − ( . ) The alternating flux φ also induces an emf, called back emf in the primary. This is p p N φ = − ( . ) But ε p = v p .
If this were not so, the primary current would be infinite since 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 ε s = v s where v s is the voltage across the secondary. Therefore, Eqs. ( .
) and ( . ) can be written as s s v N d t φ = − [ . (a)] p p v N d t φ = − [ . (a)] From Eqs.
[ . (a)] and [ . (a)], we have s s p p v N v N ( . ) FIGURE .
Two arrangements for winding of primary and secondary coil in a transformer: (a) two coils on top of each other, (b) two coils on separate limbs of the core.