Assertion (A): A very short section of high-impedance transmission line behaves like a series inductance at RF. Reason (R): A very short section of low-impedance transmission line is equivalent to a series resistance at RF.

Introduction / Context:
Lumped equivalents of electrically short transmission-line sections are widely used in impedance-matching and filter synthesis. Recognizing which line (high-Z0 or low-Z0) mimics inductance or capacitance helps build practical microwave networks without discrete components.

Given Data / Assumptions:

• Electrically short line: β l ≪ 1.
• Characteristic impedance Z0 (high vs low) and propagation constant γ ≈ jβ (low-loss).
• Operating in RF/microwave regime with small conductor/dielectric loss.

Concept / Approach:

The input impedance of a short series line (two-port viewed as series element) can be expanded. A short high-Z0 line section in series behaves like jωL (series inductance). Conversely, a short low-Z0 section used in shunt behaves like jωC (shunt capacitance). The reason statement claiming “series resistance” for a low-Z0 short section is therefore incorrect; lossless lines contribute reactance, not resistance.

Step-by-Step Solution:

Verification / Alternative check:

Smith-chart stubs: high-Z0 series lines move along inductive arcs; low-Z0 shunt stubs provide capacitive susceptance—standard matching practice.

Why Other Options Are Wrong:

• Both correct: R is not correct.
• A wrong but R correct / Both wrong: Opposite to classical short-line approximations.

Common Pitfalls:

Forgetting the role of series vs shunt configuration; conflating ohmic resistance with reactive impedance in low-loss lines.

Final Answer:

A is correct but R is wrong