Question:
A rectangular waveguide with dimensions \(a=2.5\) cm, \(b=1\) cm is operating below 15 GHz. If the guide is filled with a medium characterized by \(\sigma=0\), \(\epsilon=4\epsilon_0\), \(\mu_r=1\), calculate the cutoff frequency of dominant mode?
A rectangular waveguide with dimensions \(a=2.5\) cm, \(b=1\) cm is operating below 15 GHz. If the guide is filled with a medium characterized by \(\sigma=0\), \(\epsilon=4\epsilon_0\), \(\mu_r=1\), calculate the cutoff frequency of dominant mode?
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For rectangular waveguides,
\[
f_{c(TE_{10})}
=
\frac{c}{2a\sqrt{\mu_r\epsilon_r}}
\]
TE\(_{10}\) is always the dominant mode.
Updated On: Jun 25, 2026
- \(3\) GHz
- \(9\) GHz
- \(12\) GHz
- \(15\) GHz
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
The dominant mode in a rectangular waveguide is the TE\(_{10}\) mode.
The cutoff frequency is
\[
f_c=\frac{c}{2a\sqrt{\mu_r\epsilon_r}}
\]
where
\[
a=2.5\,cm=0.025\,m
\]
\[
\epsilon_r=4,\qquad \mu_r=1
\]
Step 1: Substitute the values into the cutoff frequency formula.
\[ f_c= \frac{3\times10^8} {2(0.025)\sqrt{4}} \] \[ = \frac{3\times10^8} {0.1} \] \[ =3\times10^9~Hz \]
Step 2: Convert into GHz.
\[ f_c=3~GHz \]
Step 3: Final Answer.
\[ \boxed{f_c=3~GHz} \] Hence, \[ \boxed{\text{Correct Option (A)}} \]
Step 1: Substitute the values into the cutoff frequency formula.
\[ f_c= \frac{3\times10^8} {2(0.025)\sqrt{4}} \] \[ = \frac{3\times10^8} {0.1} \] \[ =3\times10^9~Hz \]
Step 2: Convert into GHz.
\[ f_c=3~GHz \]
Step 3: Final Answer.
\[ \boxed{f_c=3~GHz} \] Hence, \[ \boxed{\text{Correct Option (A)}} \]
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