Question

A 220 volts input is supplied to a transformer. The output circuit draws a current 2.0 A at 440 volts. If the efficiency of transformer is 80 %, the current drawn by the input windings of a transformer is:
A)5.0 A
B)3.6 A
C)2.8 A
D)2.5 A

Answer 1

Hint: Students must know that an ideal transformer follows the law of conservation of energy. The formula of power in a transformer. The concept of efficiency in a real transformer, which undergoes losses.

Formula used: In case of an ideal transformer ${{I}_{1}}{{V}_{1}}={{I}_{2}}{{V}_{2}}$ where, the left side of equation gives input current and voltage and the right side gives their output counterparts. Incase, case of a real transformer,
$\eta =\dfrac{{{I}_{2}}{{V}_{2}}}{{{I}_{1}}{{V}_{1}}}=\dfrac{Powe{{r}_{out}}}{Powe{{r}_{in}}}$, where, $\eta $ is the efficiency of the transformer.

Complete step by step answer:
We are given that output current is 2.0 amperes and the output voltage is 440 volts. The input voltage 220 volt, and efficiency is 80 % or 0.8.
Using the formula of efficiency, we get
$\eta =\dfrac{{{I}_{out}}{{V}_{out}}}{{{I}_{in}}{{V}_{in}}}$, we want to find value of ${{I}_{in}}$
Putting the values in equation
$\begin{align}
  & {{I}_{out}}=2.0A \\
 & {{V}_{out}}=440V \\
 & {{V}_{in}}=220V \\
 & \eta =0.8 \\
\end{align}$
We get,
$0.8=\dfrac{2\times 440}{{{I}_{in}}\times 220}$
This gives us,
${{I}_{in}}=5A$

So, the correct answer is “Option A”.

Additional Information: A transformer is a passive electrical device, like resistor, capacitor and inductor.
There are two types of transformers, Step-up and Step-down transformers.
Step up transformers are used for increasing low AC voltages at high currents.
Step down transformers are used for decreasing high AC voltages at low currents.
In ideal conditions, a transformer is a lossless device which perfectly transfers the electrical energy from one side to the other side.
It is a device which uses the magnetic forces. In the primary coil, the current produces the magnetic flux, this flux is transferred to the secondary coil, which follows the Lenz law to produce current from the magnetic flux.
Just like other magnetic devices, the transformer suffers from losses like Hysteresis loss and eddy loop losses.
Due to the imperfections in manufacturing, some flux will always leak out of the transformer.
A famous special type of transformer called the Tesla coil was discovered by Nikola Tesla.

Note: Transformers are part of essentially any electrical device which has integrated circuits. Students must keep in mind that the efficiency is given in percentage form and must be converted back to fractional form before solving the problem.