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Question: A step down transformer reduces \[220V\] to \(11V\) .The primary coil draws \(5A\) current and secon...

A step down transformer reduces 220V220V to 11V11V .The primary coil draws 5A5A current and secondary coil supplies 90A90A.Efficiency of the transformer will be
A. 4.4%4.4\%
B. 20%20\%
C. 33%33\%
D. 90%90\%

Explanation

Solution

Efficiency of any instrument or device either electrical or mechanical can be given as the ratio of output by input. That means dividing the output of that particular device by its input and then the whole sum is multiplied by 100100 then we will get the efficiency percentage.

Complete step-by-step answer:
So here we know that the transformer has one primary coil and one secondary coil. The primary coil takes the input and the transformer gives its output at the secondary coil. So, the quantities related to the primary coil will give the quantities associated to the input while the quantities related to the secondary will give the quantities related to the output.
So here we will take the power as a final quantity and we will do the calculations to find the input power and output power.
So firstly, for the input power,
Input Power= Pi={P_i} = ViIi{V_i}{I_i}
Here the suffix iiis stands for initial,
As we have given Vi=220V{V_i} = 220Vand Ii=5A{I_{_i}} = 5A
So Pi=220×5=1100W{P_i} = 220 \times 5 = 1100W
Similarly, the output power,
Po=VoIo{P_o} = {V_o}{I_o}
Here suffix o stands for output.
And we have given Vo=11V{V_o} = 11Vand Io=90A{I_o} = 90A
So, Po=11×90=990W{P_o} = 11 \times 90 = 990W
Now we have both output and the input power for the transformer. So now will calculate the efficiency as follows,
As we know that, efficiency = η\eta = output power of the transformerinputpower of the transformer\dfrac{{output{\text{ }}power{\text{ }}of{\text{ }}the{\text{ }}transformer}}{{inputpower{\text{ }}of{\text{ }}the{\text{ }}transformer}}
η\eta =PoPi\dfrac{{{P_o}}}{{{P_i}}}
⇒η=1100990=0.9\Rightarrow \eta = \dfrac{{1100}}{{990}} = 0.9.
This is the efficiency of the transformer but for getting the efficiency in the percentage we will multiply 100100,
So % efficiency= η=(0.9×100)%\eta = (0.9 \times 100)\%
So η=90%\eta = 90\%
So, the efficiency of the given transformer is 90%90\% .

So, the correct answer is “Option D”.

Note: Among all the electrical devices the efficiency of the transformer is the highest. Most of the transformers have full load efficiency from 95% to 98.5%. though the value of the input and output power of the transformers doesn’t vary with a large difference but still some losses are there, those losses related to the transformer is as follows-
1. Core loss or iron loss-
(i) hysteresis loss
(ii) eddy current loss
2. Copper loss.