Question

A step-down transformer reduces the voltage of a transmission line from 2200V to 220V. The power delivered by it is 880W and its efficiency is 88%. The input current is :
A. $4.65mA$
B. $0.045$A
C. $0.45A$
D. $4.65A$

Answer 1

- Hint: In this question we will use the concept of efficiency of a step-down transformer. Here we will use the formulae for the efficiency of a transformer when the output and input power is given. The percentage efficiency of a transformer is given by: $\dfrac{{{\text{output power obtained}}}}{{{\text{input power given}}}} \times 100\%$.

Complete step-by-step solution -
Here given that ,
efficiency = 88%,
power delivered means output power = 880W,
input voltage = 2200V and output voltage = 220V.
So now we know that a step down transformer decreases the voltage but increases the current.
We have,
\Rightarrow percentage{\text{ }}efficiency = \dfrac{{{\text{output power obtained }}}}{{{\text{input power given}}}} \times 100{\text{ % }} \\\ \Rightarrow {\text{ 88% = }}\dfrac{{880W}}{{{\text{input power given}}}} \times 100% \\\ \Rightarrow {\text{input power given}} = 1000W \\\
Here we get input power = 1000W , now we have to find out input current, by using the formulae of input power. i.e.
$\Rightarrow$ $Input{\text{ }}power = (input{\text{ }}current) \times (input{\text{ }}voltage)$
$\Rightarrow$ $1000W = (input{\text{ }}current) \times 2200V$
$\Rightarrow$ = $\dfrac{{1000W}}{{2200V}} = input{\text{ }}current$
$\Rightarrow$ $input{\text{ }}current$ = 0.45A.
Hence, option (C) is the correct answer.

Note: In this type of question, first we have to remember the basic concept of efficiency of a transformer. Then we have to find out the details given in the question. Then according to the formula of efficiency, we will put all the known values in the formula and then we can find the unknown values from that. After that we will use the formula of power, we can easily find out the value of current by putting the given value of voltage and power.