GATE 2015 EE (EE2) – Question 30
Electrical Machines · Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency · 1 mark · Multiple choice
Choose transformer ratios a,b so Zin is purely resistive and equals 2.5 Ω at angular frequency 5000 rad/s.
- a=0.5,b=2.0
- a=2.0,b=0.5
- a=1.0,b=1.0
- a=4.0,b=0.5
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Correct answer: (B) a=2.0,b=0.5
Explanation
At ω=5000, capacitor reactance is −j20 Ω and inductor reactance j5 Ω. Reflect the final 2.5 Ω resistor through ratio 1:a to get 2.5/a².
The whole intermediate series impedance is then reflected by factor 1/b², so Zin=−j20+(2.5/a²+j5)/b².
Zero imaginary part requires 5/b²=20, giving b=0.5. Real part 2.5 requires a²b²=1, giving a=2. Thus **B**.
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