Question

A step down transformer, transforms a supply line voltage of 2200 V into 220 V. The primary coil has 5000 turns. The efficiency and the power transmitted by the transformer are 90% and 8 KW respectively. Then the power supplied is
$\left( A \right)$ 9.89 KW
$\left( B \right)$ 8.89 KW
$\left( C \right)$ 88.9 KW
$\left( D \right)$ 889 KW

Answer 1

- Hint: In this question use the property that efficiency of a transformer is the ratio of power received at the load end to the power supplied by the source end so use this concept to reach the solution of the question.

Complete step-by-step solution -

Given data:
Supply voltage = 2200 V
Load voltage = 220 V
Number of turns in primary coil = 500
Efficiency of transformer = 90% = (90/100)
Power transmitted i.e. power received by the load end = 8 KW
Now as we know that efficiency ($\eta $) of a transformer is the ratio of power received (${P_r}$) at the load end to the power supplied (${P_s}$) by the source end.
$ \Rightarrow \eta = \dfrac{{{P_r}}}{{{P_s}}}$
Now substitute the values we have,
$ \Rightarrow \dfrac{{90}}{{100}} = \dfrac{{8{\text{ KW}}}}{{{P_s}}}$
$ \Rightarrow {P_s} = \dfrac{{8{\text{ KW}}}}{{\dfrac{{90}}{{100}}}} = \dfrac{{800}}{{90}}{\text{ = 8}}{\text{.89 KW}}$
So the power supplied by the transformer is 8.89 KW.
So this is the required answer.

Hence option (B) is the correct answer.

Note – An interesting fact is that for an ideal transformer the power supplied by the transformer is equal to the power received as the efficiency of the ideal transformer is 100%, if not than it is not an ideal transformer it is a practical transformer and the loss in the power while transferring the power from source to load (i.e. the difference of power) is called as core loss and copper loss of the transformer.