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The velocity of traveling wave through a cable of relative permittivity 9 is
9├Ч108 m/s
3├Ч108 m/s
108 m/s
2├Ч108 m/s
108 m/s
The velocity of a traveling wave in a medium is given by the relation v=╧╡rтАЛтАЛcтАЛ, where c is the speed of light in vacuum and ╧╡rтАЛ is the relative permittivity. For a cable with ╧╡rтАЛ=9, the velocity becomes v=9тАЛ3├Ч108тАЛ=108 m/s.
The velocity of a traveling wave in a medium is given by the relation v=╧╡rтАЛтАЛcтАЛ, where c is the speed of light in vacuum and ╧╡rтАЛ is the relative permittivity. For a cable with ╧╡rтАЛ=9, the velocity becomes v=9тАЛ3├Ч108тАЛ=108 m/s.
v=╧╡rтАЛтАЛcтАЛ тАФ Calculation of wave velocity in a dielectric medium
cтЙИ3├Ч108┬аm/s тАФ Velocity of electromagnetic waves in vacuum
In electromagnetic wave propagation through a transmission line or cable, the dielectric constant (relative permittivity) slows down the wave compared to its speed in free space. Since the velocity is inversely proportional to the square root of the dielectric constant, an increase in permittivity results in a reduction of wave velocity, which is critical for calculating time delays and fault locations in power systems.
The velocity of a wave decreases as the relative permittivity of the insulating material increases.
For typical power cables, ╧╡rтАЛ ranges between 2 to 9, significantly slowing waves compared to overhead lines.
This calculation is essential for traveling wave fault locators in power systems.
Provides accurate estimation of wave propagation time.
Facilitates efficient design of insulation coordination.
Assumes a non-magnetic material (╬╝rтАЛ=1), which may vary slightly in practice.
Does not account for frequency-dependent losses (dispersion).
Traveling wave fault locators in transmission lines.
Surge impedance calculations for power system transients.
In vacuum or air, ╧╡rтАЛтЙИ1, leading to v=c.
Option A is c├Ч╧╡rтАЛтАЛ, which is dimensionally and physically incorrect. Option B is the speed of light in vacuum.
C is correct тАФ The velocity of the wave is calculated as the speed of light divided by the square root of relative permittivity, resulting in 108 m/s.
Remember that wave velocity on overhead lines is nearly 3├Ч108 m/s, whereas in cables, it is always significantly slower due to higher permittivity.