Question

A step-up transformer has a ratio of 3:2. What is the voltage in secondary, if the voltage in the primary is 30V?
A. 45V
B. 15V
C. 90V
D. 300V

Answer 1

Hint: Transformer is an electrical device that is used to convert low alternating voltage at higher current into a high alternating voltage at a lower current. There are two types of transformer one is step-up transformer which gives increased alternating voltage output and the step-down transformer which gives decreased alternating voltage output.

Complete step by step answer:
We can that the transformation ratio K is defined by $K = \dfrac{{{N_s}}}{{{N_p}}}$
Here, ${N_s}$ is the number of turns in the secondary coil and ${N_p}$ is the number of turns in the primary coil.
We also know that the relation between voltage and number of turns in the primary and secondary coil is given by,
$\dfrac{{{E_s}}}{{{E_p}}} = \dfrac{{{N_s}}}{{{N_P}}}$ ……. (I)
Here, ${E_s}$ is the voltage in the secondary coil and ${E_p}$ is the voltage in the primary coil.
In the given question we have a step-up transformer, in this case ${N_s} < {N_P}$ and also ${E_s} < {E_p}$ , therefore the ratio becomes $K > 1$.
Now, ratio of step-up transformer is given as,
\[{N_s}:{N_p} = 3:2\]
And the primary voltage ${E_p} = 30V$ (given)
By simplifying the equation (I), we can see that,
${E_s} = \dfrac{{{N_s}}}{{{N_p}}} \times {E_p}$
So we can now substitute ${E_p} = 30V$ and we will get,
${E_s} = \dfrac{3}{2} \times 30\,{\rm{V}}$
$\therefore {E_s} = 45{\rm{V}}$

Therefore, the voltage in the secondary coil is 45 V. Hence, the correct option is (A).

Additional information:
We find transformer relations from the second Faraday’s law of electromagnetic induction. It states that the magnitude of the induced e.m.f is directly proportional to the rate of change of magnetic flux linked with the coil.


Note:
For an ideal transformer, efficiency $\eta $ is 100%. But in a real transformer, the efficiency varies from 90-99%. This indicates that there are some energy losses in the transformer. It works on the principle of mutual induction. It is an economical device which is used to transmit electric power to long distances A.C. supply only. A transformer produces a humming noise due to the magnetostriction effect. Some electrical energy is lost in the form of mechanical energy to produce vibration in the core.