ISRO EC 2025 Q.25: solution and answer

Official answer: BSource: ISRO's final answer key of 15 May 2026

1. For a TE mode the wave impedance is the ratio of the transverse electric field to the transverse magnetic field: $Z_{TE}=\frac{E_t}{H_t}$.

2. Maxwell's equations for a mode travelling along the guide give $Z_{TE}=\frac{\omega \mu }{\beta }$, where $\beta$ is the guide phase constant.

3. The phase constant is $\beta =k\sqrt{1-{\left(\frac{f_c}{f}\right)}^2}$, with $k=\omega \sqrt{\mu \epsilon }$.

4. Substituting: $Z_{TE}=\frac{\omega \mu }{k\sqrt{1-(f_c/f{)}^2}}=\frac{\eta }{\sqrt{1-(f_c/f{)}^2}}$, where $\eta =\sqrt{\mu /\epsilon }$ is the intrinsic impedance of the filling medium.

5. Check: for $f>f_c$, $Z_{TE}>\eta$. As $f\to \infty$, $Z_{TE}\to \eta$. At cutoff, $Z_{TE}\to \infty$. This matches option (b).

6. Option (a) cannot be right: $E/H$ is already an impedance, so $\eta E/H$ would have units of ${\Omega }^2$. Option (c) is the TM-mode form, $Z_{TM}=\eta \sqrt{1-(f_c/f{)}^2}$, which is less than $\eta$. Option (d) is wrong because the impedance varies with frequency.