Question

To have the same cut off wave length for dominant mode of propagation for rectangular & circular wave guides

Answer 1

${\lambda }_c{|}_{rectagular}=2a$
$f_c{|}_{circular}=\frac{1}{2\pi \sqrt{{\mu }_0{\in }_0}}\frac{1.841}{r}$
$f_c{|}_{circular}=\frac{c}{2\pi }\frac{1.841}{r}$
${\lambda }_c{|}_{circular}=\frac{2\pi r}{1.841}$
${\lambda }_c{|}_{rectagular}={\lambda }_c{|}_{circular}$
$2a=\frac{2\pi r}{1.841}$
$\frac{a}{r}=1.706$