Question

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. No-load current drawn would be smaller for operation in the USA compared to that in India
• B. For the same load current, the losses would be higher in the USA compared to that in India
• C. The peak magnetic flux density in the core would be higher while operating in the USA compared to that in India
• D. The eddy current losses in the core would be approximately 44% higher while operating in the USA compared to that in India

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.

Answer 1

The Correct Option is A

Step 1: Recall the EMF equation and what stays fixed on the same core.
For a transformer,
\[ V=4.44\,f\,N\,B_{max}\,A \]
where \(f\) is the frequency, \(N\) is the number of turns, \(B_{max}\) is the peak flux density, and \(A\) is the core area. Since it is physically the same transformer moved from India to the USA, \(N\) and \(A\) do not change. So \(B_{max}\) is proportional to \(V/f\).

Step 2: Compute the ratio of peak flux density in the two countries.
\[ \frac{B_{max,USA}}{B_{max,India}}=\frac{V_{USA}/f_{USA}}{V_{India}/f_{India}}=\frac{110/60}{220/50}=\frac{1.8333}{4.4}\approx0.4167 \]
This shows the peak flux density in the USA is only about \(41.7\%\) of what it was in India, meaning it is lower, not higher. So statement (C) is false.

Step 3: Relate no-load current to flux density.
The no-load, or magnetizing, current sets up the working flux in the core. On the same unsaturated core, a smaller required flux needs a smaller magnetizing current. Since \(B_{max}\) is lower in the USA, the no-load current needed to establish it is also smaller in the USA compared to India. So statement (A) is true.

Step 4: Check the loss statement for the same load current.
Copper loss depends only on the load current and winding resistance, so it stays unchanged between the two countries for the same load current. Core loss depends on frequency and flux density, and since \(B_{max}\) drops sharply while \(f\) rises only mildly, the core loss actually falls in the USA rather than rising. So the claim that losses would be higher in the USA, statement (B), is false.

Step 5: Check the eddy current loss statement.
Eddy current loss varies as
\[ P_e\propto f^2B_{max}^2 \]
\[ \frac{P_{e,USA}}{P_{e,India}}=\left(\frac{60}{50}\right)^2\times(0.4167)^2=1.44\times0.1736\approx0.25 \]
This means the eddy current loss in the USA is only about \(25\%\) of its value in India, a large decrease, not a \(44\%\) increase. So statement (D) is false.

Step 6: Final conclusion.
Only the statement about the smaller no-load current in the USA holds up.
\[ \boxed{\text{No-load current drawn would be smaller for operation in the USA}} \]
Hence the correct option is (A).