GATE 2018 EE Q.1: solution and answer

GATE 2018 · EEQ.1 · 1 mark · MCQ

A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

(A)
4.8
(B)
6.8
(C)
8.8
(D)
10.8

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Answer and solution

ANSWER

The percentage regulation of the transformer is 4.8%, matching option (A).

Official answer: ASource: Official answer key, GATE 2018 EE (IIT Guwahati)

Step 1 — Split the impedance drop into resistive and reactive parts: The total per-unit impedance voltage drop at full load is $e_{z} = 5%$ , and the resistive part is $e_{r} = 3%$ . Since $e_{r}$ and $e_{x}$ combine as quadrature phasor components to give $e_{z}$ , $e_{z}^{2} = e_{r}^{2} + e_{x}^{2} ⟹ e_{x} = 5^{2} - 3^{2} = 25 - 9 = 16 = 4%$
Step 2 — Resolve the load power factor: For $0.8$ lagging power factor, $cos ϕ = 0.8$ and $sin ϕ = 1 - 0. 8^{2} = 0.6$ .
Step 3 — Apply the approximate regulation formula for a lagging power factor load: $% Reg = e_{r} cos ϕ + e_{x} sin ϕ$ (the reactive-drop term is added for a lagging load; it would be subtracted only for a leading load).
Step 4 — Substitute the values: $% Reg = 3 (0.8) + 4 (0.6) = 2.4 + 2.4 = 4.8%$
This matches option (A).

KEY IDEA

Total per-unit impedance drop $e_{z}$ splits into a resistive part $e_{r}$ and reactive part $e_{x}$ via $e_{z}^{2} = e_{r}^{2} + e_{x}^{2}$ (right-triangle relation, since resistance drop and reactance drop are in phase quadrature relative to the load current phasor). For lagging power factor, the approximate percentage regulation is $% Reg \approx e_{r} cos ϕ + e_{x} sin ϕ$ (a second-order correction term is negligible here and does not change the answer).

WATCH OUT FOR

Using the plus/minus sign wrong for the reactive term (lagging power factor requires the reactive-drop term to be added, not subtracted — subtraction applies to leading pf), or mis-splitting the 5% total impedance drop into resistive/reactive components using an arithmetic sum instead of $e_{z}^{2} - e_{r}^{2}$ .

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GATE 2018 EE Q.1: solution and answer

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