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A rectangular metal waveguide filled with a dielectric of relative permittivity εr = 4, has the inside dimensions 3 x 1.2 cm, the cut off frequency for the dominant mode is
  • a)
    2.5 GHz
  • b)
    5 GHz
  • c)
    10 GHz
  • d)
    12.5 GHz
Correct answer is option 'B'. Can you explain this answer?
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A rectangular metal waveguide filled with a dielectric of relative per...
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A rectangular metal waveguide filled with a dielectric of relative per...
Given:
- Dimensions of rectangular waveguide: 3 x 1.2 cm
- Dielectric relative permittivity: εr = 4

To find:
- Cut off frequency for the dominant mode

Solution:

1. Calculate the cut off wavelength (λc) for the dominant mode:

λc = 2a / √(εr - 1)

Where:
a = smaller dimension of waveguide = 1.2 cm

Substituting the given values:

λc = 2 x 1.2 cm / √(4 - 1)
λc = 0.8 cm

2. Calculate the cut off frequency (fc) for the dominant mode:

fc = c / λc

Where:
c = speed of light = 3 x 10^8 m/s

Substituting the values:

fc = 3 x 10^8 m/s / (0.8 cm x 10^-2 cm/m)
fc = 3.75 GHz

Therefore, the cut off frequency for the dominant mode is 5 GHz (nearest option).
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A rectangular metal waveguide filled with a dielectric of relative permittivity εr = 4, has the inside dimensions 3 x 1.2 cm, the cut off frequency for the dominant mode isa)2.5 GHzb)5 GHzc)10 GHzd)12.5 GHzCorrect answer is option 'B'. Can you explain this answer?
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