A single core lead covered cable is to be designed for 132

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A single core lead covered cable is to be designed for 132 kV to earth. Its conductor radius is 20 mm and its insulating material A, B and C have relative per mittivities 5, 4 and 3 respectively and corresponding maximum permissible stresses of 3.6, 2.4 and 2.0 kV/mm (rms) respectively. The minimum diameter of the lead steath will be _______ mm

1. 173.78 mm
2. 1738 mm
3. 1.7378 mm
4. 173.8 mm

Correct Option: A

g_maxA =	q
	2πε₀ε_Ar

g_{max B} =	q
	2πε₀ε_Br₁

g_{max C} =	q
	2πε₀ε_Cr₂

ε_Ar g_maxA = ε_Br₁g_{max B} = ε_Cr₂g_{max C}
or 5 × 20 × 3.6 = 4 × r₁ × 2.4 = 3 × r₂ × 2.0

∴ r₁ =	5 × 20 × 3.6	= 37.5 mm
	4 × 2.4

and r₂ =	5 × 20 × 3.6	= 60 mm
	3 × 2.0

V₁ g_{max A} r In		r₁
		r

= 3.6 × 20 × In		37.5		= 45.25 kV
		20

V₂ g_{max B} r₁ In		r₂
		r₁

= 2.4 × 37.5 × In		60		= 42.3 kV
		37.5

V₃ g_{max C} r₂ In		R
		r₂

= 2.0 × 60 × In		R
		60

Now, 132 = 45.25 + 42.30 + 120 ln		R
		60

⇒ 44.45 = 120 ln		R
		60

⇒ 0.370 = ln		R
		60

⇒ = 86.89 mm
∴ Diameter of sheath = 2R = 2 × 86.89
= 173.78 mm