A two conductor 1– φ line operates at 50 Hz. The diameter

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A two conductor 1– φ line operates at 50 Hz. The diameter of each conductor is 20 mm and the spacing between the conductors is 3m. The height of conduct or above the ground is 6m. The capacitance of the line to neutral will be ________pF/m

1. 0.97 pF/m
2. 97 pF/m
3. 97.7 pF/m
4. 9.7 pF/m

Correct Option: D

C_n =	2πε₀
	In	D	- In	H_m
		r		H_s

Here, r = 10 mm = 10 × 10^-3m,
D = 3 m, h = 6 m,
H_{1/sub> = H₂ = 2h = 12 m
H₁₂ = H₂₁ = (D² + 4h²)^1/2
= (3² + 4 × 6²)^1/2 = √153
H_m = (H₁₂ . H₂₁)^1/2 = H₁₂ = √153m
H_s = (H₁ × H₂)^1/2 = (2h. 2h)^1/2 = 2h = 12m
C_n = 2πε₀
In 3 - In √153
10 × 10^-3 12

= 1
18 × 10⁹ × In 3 × 12
10^-3 × √153

= 9.7 × 10^-12 F/m
= 9.7 pF/m}