What length of a 60 Hz transmission line is considered short?

• A. Less than approximately 25 mi (40 km)
• B. Between 25 mi (40 km) and 50 mi (80 km)
• C. Less than approximately 50 mi (80 km)
• D. More than approximately 50 mi (80 km)

Answer: (C)

In power transmission, a line is categorized as short when its length is significantly shorter than the wavelength of the electrical signal being transmitted. At a frequency of 60 Hz, the wavelength is quite long, roughly calculated using the formula ( \lambda = \frac{v}{f} ), where ( v ) is the speed of the signal (approximately the speed of light in a vacuum, about 300,000 km/s) and ( f ) is the frequency. For 60 Hz, this wavelength turns out to be around 5,000 km (over 3,100 miles).

For practical purposes, a transmission line can be considered short if it is less than about 1/10th of this wavelength. This puts the length threshold around 50 miles (approximately 80 km). Indeed, lengths under this threshold do not exhibit significant effects like capacitance and inductance in the way longer lines would.

Thus, categorizing a transmission line as short at around 50 miles aligns with the concept of its electrical characteristics being predominately resistive, making it practical to analyze without complex reactive effects. Lines longer than this tend to need more careful analysis that accounts for these reactive effects, placing them in the categories of medium or