A single phase load of 200 kVA, is delivered at 2500 V over

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A single phase load of 200 kVA, is delivered at 2500 V over a tranmissi on line having a R = 1.4Ω, X = 0.8Ω. What is the voltage at the sending end, when the power factor of the load is 0.8 lagging?

1. 2.627 kV
2. 2.069 kV
3. 2.840 kV
4. 3.54 kV

Correct Option: A

I =	200 × 1000	= 80A
	2500

Z = R + jX = 1.4 + j0.8 = 1.6 |29.74°
Let V_r is the reference phasor. Therefore
V_r = V_r + j0 = 2500 + j0
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 |7.12°
= 2500 + 128 (cos 7.12° – j sin 7.12°)
= 2500 + 127 – j 15.87
= [(2627)2 + (15.87)2]^1/2
= 2627.06 V
= 2.627 kV