Dominant transverse-electric (TE) modes: match common microwave structures to their dominant TE mode. List I (Structure) A. Rectangular waveguide B. Circular waveguide C. Rectangular cavity resonator List II (Dominant TE mode) TE101 TE10 TE111 TE11

Introduction / Context:
Understanding which mode starts first (dominant mode) in a waveguide or cavity is essential for calculating cutoff frequencies, field patterns, and bandwidth limitations in microwave engineering.

Given Data / Assumptions:

• Rectangular waveguide dimensions are a (broad wall) and b (narrow wall).
• Circular waveguide diameter determines TE/TM cutoff; the lowest is TE11.
• Rectangular cavities are closed resonators where indices along x, y, z axes define TE/TM modes.

Concept / Approach:

The dominant mode is the one with the lowest cutoff frequency. In rectangular waveguides, TE10 has the lowest cutoff (no variation along the narrow dimension). For circular waveguides, TE11 is dominant. In rectangular cavities, a common lowest TE resonance is TE101, corresponding to one half-wave variation along two axes and none along the remaining, depending on cavity dimensions.

Step-by-Step Solution:

Verification / Alternative check:

Cutoff relations: for rectangular guides f_c(TE_mn) ∝ √((m/a)^2 + (n/b)^2), minimizing with m=1, n=0 gives TE10. For circular guides, Bessel-root ordering yields TE11 as the smallest TE cutoff. Cavity resonances follow standing-wave conditions; practical cavity aspect ratios commonly make TE101 the first TE mode.

Why Other Options Are Wrong:

• Assigning TE111 to a rectangular cavity as “dominant” is often higher in frequency due to additional field variations.
• Mapping TE10 to circular guides is invalid because circular indices differ and TE11 is lower.

Common Pitfalls:

Confusing propagation modes in open guides with resonance modes in closed cavities; although notation is similar, boundary conditions and frequency ordering differ.

Final Answer:

A-2, B-4, C-1