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A single phase 10 kVA, 50 Hz transformer with 1 kV primary winding draws 0.5 A and 55 W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions √2 times the corresponding dimensions of the first transformer.The core material and lamination thickness are the same in both transformers. The primary windings of both the transformers have the same number of turns. If a rated voltage of 2 kV at 50 Hz is applied to the primary of the second transformer, then the no load current and power, respectively, are
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- 0.7 A, 77.8 W
- 0.7 A, 155.6 W
- 1 A, 110 W
- 1 A, 220 W
Correct Option: B
At no - load, I = Io
Io = Ii + Im
No - load loss, Pi = V1 .Ii
| ⇒ Ii = | = | = 0.055 Amp. | ||
| V1 | 1000 |
then, I m = √Io² + I1²
= √0.5² + 0.055² = 0.4969 Amp.
when the dimensions increased by √2 times to that of first transformer.
| Reluctance, R' = | = | = | |||
| μA'C | μ(√2)2 AC | √2 |
| and as , Im ∝ | [φ H .dl = Ni = φ R] | |
| R |
Im' = 0.4969 √2 = 0.702 Amp.
Losses are directly proportional to the volume, since
for, pe = Ke f2 Bm2 [Eddy current loss], and
for, ph = Kh f2 Bmh [hysteris loss],
Ke, Kh ∝ volume of material
then , p i' = (√2)3 × 55 = 155.6 W
| ⇒ Ii' = | = 0.077 | |
| 2 × 103 |
No load current,
Io = √Ii'² + Im'² = 0.70 Amp.
