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Describe the construction and working of a transformer and hence obtain the relation for \(\left(\frac{v_s}{v_p}\right)\) in terms of number of turns of primary and secondary.

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Construction: It consists of laminated core of soft iron, on which two coils of insulated copper wire are separately, wound. These coils are kept insulated from each other and from the iron-core, but are coupled through mutual induction. The number of turns in these coils are different. Out of these coils one coil is called primary coil and other is called the secondary coil. The terminals of primary coils are connected to ac mains and the terminals of the secondary coil are connected to external circuit in which alternating current of desired voltage is required. 

Transformers are of two types:

Construction: 

(a) Step up Transformer: It transforms the alternating low voltage to alternating high voltage and in this the number of turns in secondary coil is more than that in primary coil (i.e., NS > NP).

(b) Step down Transformer: It transforms the alternating high voltage to alternating low voltage and in this the number of turns in secondary coil is less than that in primary coil (i.e., NS < NP). 

Working: When alternating current source is connected to the ends of primary coil, the current changes continuously in the primary coil; due to which the magnetic flux linked with the secondary coil changes continuously, therefore the alternating emf of same frequency is developed across the secondary.

Let NP be the number of turns in primary coil, NS the number of turns in secondary coil and φ the magnetic flux linked with each turn. We assume that there is no leakage of flux so that the flux linked with each turn of primary coil and secondary coil is the same. According to Faraday's laws the emf induced in the primary coil.

\(\epsilon _P = -N_P \frac{\Delta \phi}{\Delta t}\)  …(i)

and emf induced in the secondary coil.

\(\epsilon = -N_s \frac{\Delta \phi}{\Delta t}\) …(ii)

From (i) and (ii)

\(\frac{\epsilon _S}{\epsilon _ P} = \frac{N_S}{N_P}\) …(iii)

For step up transformer \(\epsilon _S > \ \text{as} \ N_S > N_P\)

\(\epsilon _S < \epsilon_P \ \text{as} \ N_S < N_P\)

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