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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
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