A single circuit 50 Hz, 3 – φ transmission line has

A single circuit 50 Hz, 3 – φ transmission line has the following parameters per km.
R = 0.2Ω, L = 1.3 mH, C = 0.01 µF
The efficiency of the line, if the line is 120 km long and deliver 40 mW at 132 kV and 0.8 pf lagging will be _________%

R = 0.2 × 120 = 24Ω
X_L = 2πƒ. L = 314 × 120 × 1.30 × 10^-3
= 48.98Ω
X_C = 0.01 × 10^-6 × 120 = 12

I_r =	40 × 1000	= 218.7 Amp
	√3 × 132 × 0.8

I_r = 218.7 (0.8 – j0.6) = (174.96 – j131.22)
I_C1 = (j314)_r0.6 × 10^–6 × V_r

V_r =	132 × 1000	= 76200 volts
	√3

I_C1 = (j314) × 0.6× 10^-6 × 76200 = (j14.356) amp
I_L = I_C1 + I_r = (174.96 – j116.86)
= 210.39 |33.73°
loss = 3 × (210.39)² × 24 = 3.187 MW.

η =	40 × 100	=	40 × 100	= 92.6%
	(40 + 3.187		43.187