GATE 2023 IN – Question 58
A single-phase transformer is short-circuit tested at 1 kHz with its secondary shorted. The wattmeter reads 8 W, primary current is 2 A, and primary voltage 6 V. Neglect no-load loss and current; the core is linear. Keeping the secondary shorted, connect the primary to a 2 V RMS, 1 kHz source in series with capacitance $1/(2\pi\sqrt5)$ mF. The primary RMS current is ______ A (two decimal places).
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Correct answer: 0.95 to 1.05
Explanation
Short-circuit data give $R_{eq}=P/I^2=8/4=2$ Ω and $|Z_{eq}|=V/I=3$ Ω.
Therefore $X_{eq}=\sqrt{3^2-2^2}=\sqrt5$ Ω. At 1 kHz, the specified capacitor has $X_C=\sqrt5$ Ω, cancelling the leakage reactance. Remaining impedance is 2 Ω, giving $I=2/2=\boxed{1.00}$ A.