Question

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

Hint:

The voltage ratio in a transformer is directly proportional to the ratio of the number of turns in the secondary and primary coils. This relationship allows the transformer to step up or step down voltage.

Answer 1

Step 1: Construction of a Transformer:
A transformer consists of two coils, the primary coil and the secondary coil, wound on a common iron core. The core is usually made of soft iron to provide a low reluctance path for the magnetic flux. The primary coil is connected to the AC supply, and the secondary coil provides the output voltage.
Step 2: Working of a Transformer:
When an alternating current (AC) is passed through the primary coil, it generates an alternating magnetic flux. This flux passes through the iron core and induces an alternating voltage in the secondary coil through electromagnetic induction. The voltage induced in the secondary coil depends on the number of turns in the primary and secondary coils.
Step 3: Derivation of the Relation for Voltage:
According to Faraday’s law of electromagnetic induction, the induced emf (electromotive force) in a coil is proportional to the rate of change of magnetic flux linkage. Thus, for the primary coil, the induced emf is:
\[ V_p = N_p \frac{d\Phi}{dt} \] where \( N_p \) is the number of turns in the primary coil and \( \Phi \) is the magnetic flux.
Similarly, for the secondary coil:
\[ V_s = N_s \frac{d\Phi}{dt} \] where \( N_s \) is the number of turns in the secondary coil.
Since the rate of change of magnetic flux linkage is the same in both coils, we can equate the expressions for \( V_p \) and \( V_s \):
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \] Thus, the ratio of the voltages in the secondary and primary coils is equal to the ratio of the number of turns in the secondary and primary coils.
Conclusion:
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \]