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A 3-phase transmission line has its conductors at the corners of an equilateral triangle with side 3 m. The diameter of each conductor is 1.63 cm. The inductance of the line per phase per km is
  • a)
    1.232 mH
  • b)
    1.182 mH
  • c)
    1.093 mH
  • d)
    1.043 mH
Correct answer is option 'A'. Can you explain this answer?
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Given parameters:

- 3-phase transmission line
- Conductors at the corners of an equilateral triangle with side 3 m
- Diameter of each conductor = 1.63 cm
- Inductance of the line per phase per km = ?

Approach:

- Calculate the radius of each conductor
- Calculate the distance between the conductors
- Calculate the geometric mean radius (GMR) of the conductors
- Use the formula for inductance per phase per km of a 3-phase transmission line

Calculation:

- Radius of each conductor = 1.63/2 = 0.815 cm = 0.00815 m
- Distance between the conductors = 3 m
- Geometric mean radius (GMR) of the conductors = sqrt(3)*0.00815 = 0.0141 m
- Formula for inductance per phase per km of a 3-phase transmission line: L = 2x10^-7 * ln(D/GMR) H/km
- L = 2x10^-7 * ln(3.00815/0.0141) = 1.232 mH/km

Therefore, the inductance of the line per phase per km is 1.232 mH (option A).
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A 3-phase transmission line has its conductors at the corners of an equilateral triangle with side 3 m. The diameter of each conductor is 1.63 cm. The inductance of the line per phase per km isa)1.232 mHb)1.182 mHc)1.093 mHd)1.043 mHCorrect answer is option 'A'. Can you explain this answer?
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