The guided wavelength of a TEM wave in a waveguide having a wavelength of 5 units

A waveguide is a structure used to guide electromagnetic waves along a path. It is commonly used in various applications such as telecommunications, radar systems, and microwave technology. In a waveguide, there are different types of wave modes that can propagate, including Transverse Electric (TE), Transverse Magnetic (TM), and Transverse Electromagnetic (TEM) modes.

TEM Waves
A TEM wave is a type of electromagnetic wave that has both electric and magnetic field components perpendicular to the direction of wave propagation. In a TEM wave, the electric and magnetic fields are always orthogonal to each other and the direction of wave propagation.

Guided Wavelength
The guided wavelength of a wave in a waveguide is the wavelength of the wave when it is traveling inside the waveguide. It is different from the free-space wavelength, which is the wavelength of the wave in free space.

Relation between Guided Wavelength and Free-Space Wavelength
The guided wavelength in a waveguide is related to the free-space wavelength by the following equation:

Guided Wavelength = Free-Space Wavelength / √(1 - (λg / λ)^2)

Where λg is the guided wavelength and λ is the free-space wavelength.

Solution
In the given question, the free-space wavelength is given as 5 units. To find the guided wavelength, we need to substitute the values in the equation mentioned above.

Guided Wavelength = 5 / √(1 - (λg / 5)^2)

Since the guided wavelength is also given as 5 units, we can substitute this value in the equation.

5 = 5 / √(1 - (5 / 5)^2)

Simplifying the equation,

5 = 5 / √(1 - 1^2)

5 = 5 / √(1 - 1)

5 = 5 / √0

As the denominator becomes zero, the equation becomes undefined. Therefore, the guided wavelength cannot be determined, and the correct answer is option 'C' (5).

In summary, for a TEM wave in a waveguide, the guided wavelength is equal to the free-space wavelength, which is 5 units in this case.