Question

Draw a labeled diagram of a step-up transformer and explain how it works. State two characteristics of the primary coil as compared to its secondary coil.

Answer 1

Hint : To answer this question, we have to consider an alternating voltage source at the primary coil and obtain its relation with the flux linkage. Then we have to obtain the voltage at the secondary coil using Faraday’s law.

Complete step by step answer
Let us consider the transformer as shown below.

As we can see that there are coils wound on both the primary and the secondary sides of the transformer. Let there be $ {N_1} $ turns on the primary side and $ {N_2} $ turns on the secondary side.
Now across the primary coil, an alternating voltage is applied, which results in an alternating current through the primary coil. Since there is alternating current in the circuit so changing magnetic field is produced through each turn of the coil which results in an alternating flux. Let this flux be $ \varphi $ . So the emf applied and the alternating flux can be related by the Faraday’s law as
 $\Rightarrow {e_1} = {N_1}\dfrac{{d\varphi }}{{dt}} $ .................................(1)
This alternating flux is linked to the secondary coil through the iron core. We know that when an alternating flux is passed through a coil, then an emf is induced across it. This emf is given by
 $\Rightarrow {e_2} = {N_2}\dfrac{{d\varphi }}{{dt}} $ .................................(2)
Dividing (2) by (1) we get
 $\Rightarrow \dfrac{{{e_2}}}{{{e_1}}} = \dfrac{{{N_2}}}{{{N_1}}} $ .................................(3)
According to the question, the transformer is step-up. So this means that the emf in the secondary coil is greater than that in the primary coil. So we have
 $\Rightarrow {e_2} > {e_1} $
 $ \Rightarrow \dfrac{{{e_2}}}{{{e_1}}} > 1 $
From (3)
 $\Rightarrow \dfrac{{{N_2}}}{{{N_1}}} > 1 $
 $ \Rightarrow {N_2} > {N_1} $
So for a step up transformer, the number of turns in the secondary coil is greater than that of the primary coil.
So from above we see that the two characteristics of a step-up transformer are:
-The emf across the secondary is greater than that of the primary.
-The number of turns at the secondary is greater than that at the primary.

Note
A transformer is mainly used to step up or step down the level of voltage, keeping the same power. It is also used for increasing and decreasing the value of the impedance of an AC circuit.