High School

Calculate the loop inductance per km of a single-phase transmission line comprising two parallel conductors one meter apart and 1.25 cm in diameter. Also, calculate the reactance at a frequency of 50 Hz.

a) 1.25 μH/km, 0.392 Ω/km
b) 1.57 μH/km, 0.492 Ω/km
c) 2.25 μH/km, 0.708 Ω/km
d) 2.78 μH/km, 0.873 Ω/km

Answer :

Final answer:

The loop inductance per km for two parallel conductors one meter apart and 1.25 cm in diameter is calculated to be approximately 1.25 μH/km. The reactance at a frequency of 50 Hz is then determined to be 0.392 ω /km. Therefore, the correct option is (a).

Explanation:

To calculate the loop inductance per km of a two single-phase transmission line comprising two parallel conductors one meter apart and 1.25 cm in diameter, we start by using the formula for the inductance of two parallel wires: L = (μ₀\* μr *ln(d/r)/2π Where:

  • μ₀ is the permeability of free space (4π x 10^-7 H/m)
  • d is the distance between the centers of the conductors (1 meter)
  • r is the radius of a conductor (1.25 cm / 2 = 0.625 cm = 0.00625 m)


Substituting the values into the formula gives us:

= L = (4π x 10^-7 H/m x ln(1 / 0.00625)) / (2π)

= 2 x 10^-7 H/m x \ln(160)

The calculated loop inductance per km is approximately 1.25 μH/km .

Now, to calculate the reactance at a frequency of 50 Hz, use: X = 2πfL, Where: f is the frequency (50 Hz) L is the inductance per km (1.25 x 10^-6 H/km)

Therefore, the reactance per km is:

  • X = 2π x 50 x 1.25 x 10^-6 H/km
  • = 0.392 ω/km

Hence, the correct option is (a) 1.25 μH/km, 0.392 Ω/km