A 1 – φ load of 200 kVA is delivered at 2500 V over

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A 1 – φ load of 200 kVA is delivered at 2500 V over a transmission line having R = 1.4 Ω, X = 0.8 Ω. What is the power at the sending end when the power factor of the load is 0.8 leading?

1. 0.8 leading
2. 0.82 (leading)
3. 0.82 (lagging)
4. 0.6 (lagging)

Correct Option: B

I =	200 × 1000	= 80A
	2500

Z = R + jX = 1.4 + j0.8 = 1.6 |29.74°
cos φ = 0.8 (lagging)
φ_r = 36.86° (lagging)
I_r = I_r |+φ_r = 80 |+36.86°
V_s = V_r + ZI_r
= 2500 + 1.6 × |29.74° × (80 × |36.86°)
= 2500 + 128 |66.61°
= 2500 + 128 (cos 66.61° + jsin 66.61°)
= 2500 + 50.8 + j117.84
= (2550.8 + j117.84)

= 2553.5 tan^-1		117.84
		2550.8

= 2553.5 |2.63°
φ_s = 2.63° + 36.86° = 34.23°
cos φ_s = cos 34.23° = 0.82 (leading)