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A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given by
  • a)
    1.557 cm '
  • b)
    1.246 cm
  • c)
    1.6 cm
  • d)
    0.623 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A single-phase, two wire transmission line, 15 km long, is made up of ...
The fictitious conductor is one whose radius is r' and whose diameter is therefore,
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A single-phase, two wire transmission line, 15 km long, is made up of ...
Given data:
Length of transmission line, l = 15 km = 15000 m
Radius of round conductors, r = 0.8 cm = 0.008 m
Separation between conductors, d = 40 cm = 0.4 m

To find: Equivalent diameter of a thin-walled conductor having the same inductance as the original line.

Formula used:

Inductance per unit length of a two-wire transmission line is given by:
L = μ/2π ln(D/d)
Where,
μ = Permeability of free space = 4π × 10^-7 H/m
D = Distance between the centers of the two conductors
d = Diameter of each conductor

Equivalent diameter of a thin-walled conductor having the same inductance as the original line is given by:
D' = 2 √(d/2) √(D/d - 1)

Calculation:

Distance between the centers of the two conductors, D = d + separation distance = 0.4 + 0.008 = 0.408 m

Inductance per unit length of the transmission line, L = μ/2π ln(D/d)
= (4π × 10^-7)/(2π) ln(0.408/0.008)
= 5.545 × 10^-7 H/m

Equivalent diameter of a thin-walled conductor having the same inductance as the original line, D' = 2 √(d/2) √(D/d - 1)
= 2 √(0.008/2) √(0.408/0.008 - 1)
= 0.01246 m = 1.246 cm

Therefore, the equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is 1.246 cm, which is given in option B.
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Community Answer
A single-phase, two wire transmission line, 15 km long, is made up of ...
Patrick Tembo
Mr .calculus

2r'=2re^-1/4
=2*0.8*0.7788
=1.246cm
kale bwangu
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A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cm 'b)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer?
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A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cm 'b)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cm 'b)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cm 'b)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer?.
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