Question:hard
A 220V/12V single-phase transformer is designed for use in India and rated 100 VA at 50 Hz. Later, this unit is shipped to the USA where it is used as a 110V/6V transformer at 60 Hz.
Which of the following statements is/are correct?
A 220V/12V single-phase transformer is designed for use in India and rated 100 VA at 50 Hz. Later, this unit is shipped to the USA where it is used as a 110V/6V transformer at 60 Hz.
Which of the following statements is/are correct?
Which of the following statements is/are correct?
Show Hint
Since Bmax is proportional to V/f and the core stays the same, work out how Bmax, the magnetizing current, and the core losses all scale between the 220V/50Hz and 110V/60Hz operating points.
Updated On: Jul 20, 2026
- No-load current drawn would be smaller for operation in the USA compared to that in India
- For the same load current, the losses would be higher in the USA compared to that in India
- The peak magnetic flux density in the core would be higher while operating in the USA compared to that in India
- The eddy current losses in the core would be approximately 44% higher while operating in the USA compared to that in India
Show Solution
The Correct Option is A
Solution and Explanation
Step 1: Track the V/f ratio.
The peak flux density in a transformer core follows $B_{max}\propto V/f$, since $N$ and the core area stay fixed for the same physical unit. India: $V/f=220/50=4.4$. USA: $V/f=110/60\approx1.833$.
Step 2: Get the flux ratio.
\[ \frac{B_{USA}}{B_{India}}=\frac{1.833}{4.4}\approx0.417 \]
So the core runs at less than half its Indian flux density when used in the USA. This immediately rules out option (C), which claims a higher flux density.
Step 3: Link flux to the no-load current.
A lower required flux on an unsaturated core needs a correspondingly smaller magnetizing current to produce it, so the no-load current is smaller in the USA. Option (A) holds.
Step 4: Check core loss trends.
Both hysteresis loss and eddy current loss depend heavily on $B_{max}$, which has dropped a lot, more than making up for the modest rise in frequency. So total core loss falls in the USA, and copper loss for the same load current is unchanged, so total losses do not rise. Option (B) fails.
Step 5: Compute the eddy current figure directly.
\[ \frac{P_{e,USA}}{P_{e,India}}=\left(\frac{60}{50}\right)^2(0.417)^2\approx1.44\times0.174\approx0.25 \]
The eddy current loss drops to about a quarter of its Indian value, the opposite of the 44% rise claimed in option (D).
Step 6: Conclude.
The only statement that survives is the smaller no-load current in the USA.
\[ \boxed{\text{No-load current would be smaller in the USA}} \]
The peak flux density in a transformer core follows $B_{max}\propto V/f$, since $N$ and the core area stay fixed for the same physical unit. India: $V/f=220/50=4.4$. USA: $V/f=110/60\approx1.833$.
Step 2: Get the flux ratio.
\[ \frac{B_{USA}}{B_{India}}=\frac{1.833}{4.4}\approx0.417 \]
So the core runs at less than half its Indian flux density when used in the USA. This immediately rules out option (C), which claims a higher flux density.
Step 3: Link flux to the no-load current.
A lower required flux on an unsaturated core needs a correspondingly smaller magnetizing current to produce it, so the no-load current is smaller in the USA. Option (A) holds.
Step 4: Check core loss trends.
Both hysteresis loss and eddy current loss depend heavily on $B_{max}$, which has dropped a lot, more than making up for the modest rise in frequency. So total core loss falls in the USA, and copper loss for the same load current is unchanged, so total losses do not rise. Option (B) fails.
Step 5: Compute the eddy current figure directly.
\[ \frac{P_{e,USA}}{P_{e,India}}=\left(\frac{60}{50}\right)^2(0.417)^2\approx1.44\times0.174\approx0.25 \]
The eddy current loss drops to about a quarter of its Indian value, the opposite of the 44% rise claimed in option (D).
Step 6: Conclude.
The only statement that survives is the smaller no-load current in the USA.
\[ \boxed{\text{No-load current would be smaller in the USA}} \]
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