GATE 2020 IN Q.18: solution and answer

Official answer: 1.7 to 1.8Source: Official answer key, GATE 2020 IN (IIT Delhi)

1. Supply convention: a three-phase supply quoted as 400 V means the line-to-line voltage. So $V_L=400\text{V}$ (rms).

2. In a delta connection each resistor is connected directly between two lines, so the phase voltage equals the line voltage: $V_{ph}=V_L=400\text{V}$.

3. Ohm's law for one phase: $I_{ph}=\frac{V_{ph}}{R}=\frac{400}{400}=1\text{A}$. The load is purely resistive, so this current is in phase with its phase voltage.

4. Line current in a balanced delta (KCL at a delta node): each line current is the phasor difference of two phase currents that are $120^{\circ }$ apart, so its magnitude is $I_L=\sqrt{3}{I}_{ph}$.

5. $$I_L=\sqrt{3}\times 1=1.732\text{A}\approx 1.7\text{A}$$

6. Power check: $P=3\frac{V_{ph}^2}{R}=3\times \frac{400^2}{400}=1200\text{W}$, and $P=\sqrt{3}{V}_L{I}_L\cos \varphi =\sqrt{3}\times 400\times 1.732\times 1=1200\text{W}$. The two agree.