Question

A step down transformer reduces 220V to 110V. The primary and secondary currents are 5A and 9A respectively. The efficiency of transformer is:
$ (A)20\% $
$ (B)4\% $
$ (C)90\% $
$ (D)100\% $

Answer 1

Hint: A step down transformer is a kind of transformer that converts high-voltage low-current input at the primary side to low-voltage high-current output at the secondary side. In a step-down transformer, the number of coil rewinds is greater at the primary side and lower at the secondary side. It functions just opposite to a step-up transformer.

Complete step-by-step solution:
We will first assign some terms which are to be used later in our equations.
Let the primary voltage input of the step-down transformer be given by ${{E}_{P}}$ .Then, the value of ${{E}_{P}}$ is given to us as:
$\Rightarrow {{E}_{P}}=220V$
Now, let the secondary voltage input of the step-down transformer be given by ${{E}_{S}}$ .Then, the value of ${{E}_{S}}$ is given to us as:
$\Rightarrow {{E}_{s}}=110V$
Also for the currents, let the primary current input of the step-down transformer be given by ${{I}_{P}}$ .Then, the value of ${{I}_{P}}$ is given to us as:
$\Rightarrow {{I}_{P}}=5A$
And lastly, let the secondary current input of the step-down transformer be given by ${{I}_{S}}$ .Then, the value of ${{I}_{S}}$ is given to us as:
 $\Rightarrow {{I}_{S}}=9A$
Now, we know that the efficiency of a step-down transformer is given by the product of ratios of primary voltage to secondary voltage and primary current to secondary current. Mathematically, this statement could be written as:
$\Rightarrow \eta =\dfrac{{{E}_{S}}{{I}_{S}}}{{{E}_{P}}{{I}_{P}}}$
Thus efficiency percentage will be equal to:
$\Rightarrow %\eta =\dfrac{{{E}_{S}}{{I}_{S}}}{{{E}_{P}}{{I}_{P}}}\times 100$
Putting the values of terms in right hand side of the equation, we get:
$\begin{align}
  & \Rightarrow \eta =\dfrac{110\times 9}{220\times 5}\times 100 \\
 & \Rightarrow \eta =\dfrac{9}{10}\times 100 \\
 & \therefore \eta =90\% \\
\end{align}$
Hence, the efficiency of the step-down transformer comes out to be 90%.
Hence, option (C) is the correct option.

Note: Transformers are one of the only electrical equipment which have a very high efficiency of more than 90% in practical use. Also, Step-down transformers are the most widely used transformer that we come across in our day to day lives. Our local community transformer is an example of a step-down transformer.