A three phase circuit line consists of 7/4.75 mm hard drawn

Home » Power Systems » Power systems miscellaneous » Question

A three phase circuit line consists of 7/4.75 mm hard drawn copper conductors. The arrangement is shown in the figure. The line is completely transposed. What is the inductance, per phase per km of the system?

1. 0.90 mH/km
2. 0.21 mH/km
3. 0.57 mH/km
4. 0.64 mH/km

Correct Option: D

Diameter of each conductor = 3 × 4.75 = 14.25 mm.
r = 7.125 × 10^-3 m.
D_ab = √3² + 1.5² = 3.354 m
D_bc = D_a'b' = D_b'c' = 3.354 m
D_ab' = √3² + 7.5² = 8.077 m
D_bc' = D_ba' = D_b'c = D_ab' = 8.077 m
D_aa' = √6² + 6² = 6√2 m
D_cc' = 6√2 m
D_m = (D_ab.D_bc.D_ca.D_ab'.D_b'c.D_c'a.D_a'b'.D_b'c'.D_c'a'.)^1/2
= (3.354 × 3.354 × 6 × 8.076 × 8.076 × 6 × 8.076 × 8.076 × 6 × 3.354 × 3.54 × 6)^1/12
= 5.4576 m
D_sL = (r'³ × D_aa' × D_bb' × D_cc')^1/6
= [(0.7788 × 7.125 × 10^-3)³ × 6√2 × 9 × 6√2]^1/6
= 0.21913 m

= 2 × 10^-7 In		D_m
		D_sL

= 2 × 10^-7 In		5.4576		H/m
		0.21913

= 6.43 × 10^-7 H/m = 6.43 × 10^-4 H/km = 0.643 mH/k m.