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# A transformer is used to light a 100W and 110V lamp from 220V mains. If the main current 0.5A, efficiency of transformer is:A) 10%B) 50%C) 60%D) 90%

Last updated date: 17th Apr 2024
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Hint: Efficiency of transformer is given by:
$\eta = \dfrac{{output}}{{input}}$
It is the ratio of output power to input power. Generally the efficiency is maximum (with fewer losses) because the transformer is a static device.

Complete step by step solution:
Let’s discuss transformers first:
Transformer is a static device which works on the principle of electromagnetic induction. A single phase transformer has two windings primary and secondary winding .Winding having large number of turns have high voltage and the winding having less number of turns have low voltage, because voltage in a winding is directly proportional to the number of turns it has. An ideal transformer has negligible or no losses.

Now comes to the numerical part:
Transformer is used to light 100W lamps having 110V from 220 V mains.
Therefore, the output power which a transformer can give is 100W

Input power is given as:
Mains voltage given = 220V
Mains current = 0.5A
Input Power =220$\times$ 0.5=110 VA
Efficiency is calculated as:
$\Rightarrow \eta = \dfrac{{100}}{{110}} \\ \Rightarrow \eta = .909 \\ \Rightarrow \eta = .909 \times 100 = 90.9\% \\$ (we have substituted the value of input and output power)
Efficiency of the transformer is 90%.

Option (D) is correct.

Note: Transformer has two types of core named core type and shell type. Transformer core is generally made up of high permeability and low loss material like CRGO silicon steel (cold rolled grain oriented). Shell type transformers are used for low voltage applications while core type transformers are used for high voltage applications.