GATE EE 2014 Set 1 — Question 22
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Electrical Machines → Magnetic Circuits & Inductance → Construction & Principle
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Question
For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is
Correct answer
(C) 2
Solution
The no-load current is dominated by the magnetizing current .
The magnetizing current is given by .
From the EMF equation, , which gives .
Substituting into the expression:To maintain the same for a fixed and , the product must be constant.
The cross-sectional area is proportional to the square of the radius ().
If the radius is reduced by half (), the area becomes one-fourth ().
To keep constant:Thus, the number of turns must change by a factor of 2.
The magnetizing current is given by .
From the EMF equation, , which gives .
Substituting into the expression:To maintain the same for a fixed and , the product must be constant.
The cross-sectional area is proportional to the square of the radius ().
If the radius is reduced by half (), the area becomes one-fourth ().
To keep constant:Thus, the number of turns must change by a factor of 2.
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