Question

The diagram shows a transformer connected to a $240V$ A.C supply. What is the potential difference across the secondary coil of the transformer?

A. $30V$
B. $120V$
C. $240V$
D. $480V$

Answer 1

Hint: In order to solve this question we need to understand the transformer. So the transformer works on the principle of mutual induction. According to the principle of mutual induction, if there is flux change in one loop due to another loop then a emf would be induced in that loop. It is based on Faraday’s law of electromagnetic induction which states that if there is a flux change through loop and an emf would be induced in that loop, now the flux change could be done in three ways, either vary the magnetic field through loop, or vary the area of loop inside magnetic field and also by changing orientation of loop in magnetic field.

Complete step by step answer:
According to the given figure, Number of turns in Primary coil is ${N_1} = 60$.
And Number of turns in Secondary coil is ${N_2} = 30$.
Voltage across the primary coil is, ${V_1} = 240V$.
Let the voltage across the secondary coil be ${V_2}$.
Since the magnetic field through both the loops is same , the same flux through that loop, hence according to faraday’ law, emf through the second loop is due to change in flux of the first loop and vice versa.So by using transformer formula we get,
\[{V_1}{N_2} = {V_2}{N_1}\]
So voltage across secondary coil is,
\[{V_2} = \dfrac{{{V_1}{N_2}}}{{{N_1}}}\]
Putting values we get,
\[{V_2} = \dfrac{{(240)(30)}}{{(60)}}\]
\[\therefore {V_2} = 120\,V\]

So the correct option is B.

Note: It should be remembered that emf induced in loop bounds current to flow in direction, in accordance with Lenz’s law. According to Lenz’s law, current induced in the loop flows in such a direction so as to oppose the cause of its generation. For example if the flux is increasing through a loop then it would flow in that direction so that it opposes the rise in flux.