What is the charging kVAr taken by a 10 km length of the

What is the charging kVAr taken by a 10 km length of the cable when connected to an 11 kV, 50 Hz supply? The capacitance measured between any two cores of a three phase belted cable is 0.5 µF/km.

Let C_L be the capacitance between any two cores.

C_L =	C₀
	2

C₀ = 2 C_L = 2 × 0.5 × 10 = 10µF

I_C = V_p.ω.C₀ =	V_L	ω.2C_L
	√3

Total charging kVAr
= √3 (V_L).(L_C) × 10^-3

= √3 × V_L ×	V_L	× 2C_L × 10^-3
	√3

= 2 (V_L)². ω. C_L × 10^-3

= 2 × (11000)² × 2π × 50 ×	10	× 10^-3 × 10^-6
	2

= 380 kVAr.