Question

Primary winding and the secondary winding of a transformer have 100 and 300 turns respectively. If its input power is 60W then output power of the transformer will be
$(a){\text{ 240W}} \\\ (b){\text{ 180W}} \\\ (c){\text{ 60W}} \\\ (d){\text{ 20W}} \\\$

Answer 1

Hint – In this question use the direct relationship between the ratios of the secondary to the primary winding with the ratio of the secondary voltage to that of input voltage that is $\dfrac{{{V_s}}}{{{V_i}}} = \dfrac{{{N_s}}}{{{N_i}}} = \dfrac{1}{a}$. Then the transformation ratio of power in a transformer is given as$\dfrac{{{p_s}}}{{{p_i}}} = \dfrac{1}{a}$, this will help getting the right answer.

Complete step-by-step answer:

Given data:
Number of turns in the primary winding, ${N_i}$ = 100
And the number of turns in the secondary winding, ${N_s}$ = 300
Input power of the transformer = ${P_i} = 60W$
So the ratio of number of turns (i.e. secondary to primary)
$\Rightarrow \dfrac{{{N_s}}}{{{N_i}}} = \dfrac{{300}}{{100}} = \dfrac{3}{1}$
So the transformation ratio of the transformer is ($3:1$) now compare it from standard transformation ratio ($1:a$)
$\Rightarrow \dfrac{{{V_s}}}{{{V_i}}} = \dfrac{{{N_s}}}{{{N_i}}} = \dfrac{1}{a} = \dfrac{3}{1}$, where ${V_s},{V_i}$ are the secondary and primary voltage of the transformer respectively.
$\Rightarrow a = \dfrac{1}{3}$
Now the transformation ratio of power in a transformer is given as
$\Rightarrow \dfrac{{{p_s}}}{{{p_i}}} = \dfrac{1}{a}$
Now substitute the values we have,
$\Rightarrow \dfrac{{{p_s}}}{{60}} = \dfrac{1}{{\dfrac{1}{3}}} = 3$
$\Rightarrow {P_s} = 60 \times 3 = 180W$
So this is the required answer.
Hence option (B) is the correct answer.

Note – There are in practical two types of transformers that are step up and step down transformers. In a step up transformer the number of secondary windings must be greater than the number of turns in primary winding. However in a step down transformer the number of turns in primary winding must be greater than the number of turns in secondary winding.