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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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For a 500 Hz frequency excitation, a 100 km long power line will be modeled as
Short line
Medium line
Long line
None of above
Long line
Given: Frequency f = 500 Hz, Length l = 100 km. Standard transmission line speed v is approximately 3 ×10⁸ m/s.
Frequency f = 500 Hz, Length l = 100 km. Standard transmission line speed v is approximately 3 ×10⁸ m/s.
λ=fv,β=λ2π
Calculate Wavelength
Determine the wavelength of the signal at 500 Hz using the velocity of electromagnetic waves in a conductor.
λ=5003×108=600,000 m=600 km
Determine Propagation Constant
The propagation constant β (phase shift constant) is given by 2π/λ.
β=6002π≈0.01047 rad/km
Evaluate Line Classification
A line is considered long if βl>8π (roughly 22.5° or 0.39 radians). Here, βl=0.01047×100=1.047 radians, which is significantly greater than 0.39 radians.
βl=1.047 rad>0.39 rad
C is correct because the electrical length of the line at 500 Hz is large enough that the distributed parameter effects dominate, classifying it as a long line.
In power systems, a line is short if length < 80 km at 50 Hz. At higher frequencies, the wavelength decreases significantly, making even short physical lengths act as long lines due to the increased electrical phase shift.