Assertion (A): The condition for a distortionless transmission line is L = (R * C) / G. Reason (R): Line loading refers to adding series inductance to help meet the distortionless-line condition.

Introduction / Context:
The distortionless condition in transmission-line theory ensures that signals propagate without waveform distortion. It imposes a specific relationship among primary constants R, L, G, and C so that attenuation is independent of frequency and phase velocity is constant.

Given Data / Assumptions:

• Primary line constants: R (series resistance per unit length), L (series inductance per unit length), G (shunt conductance per unit length), C (shunt capacitance per unit length).
• Goal: Identify the correctness of the assertion and the reason.

Concept / Approach:

The correct Heaviside distortionless condition is R/L = G/C (equivalently L/C = R/G when all quantities are positive and finite). This makes the propagation constant's real part independent of frequency and the phase constant proportional to frequency.

Step-by-Step Solution:

Verification / Alternative check:

In telephony, adding loading coils increased L to approximate R/L ≈ G/C, which improved voice-band fidelity over long pairs. Practical designs show flatter group delay and reduced dispersion when the Heaviside condition is approximated.

Why Other Options Are Wrong:

• Both A and R correct: A is false because the stated equality is wrong.
• Both correct but not explanatory: Invalid since A is false.
• A correct, R wrong: Opposite of the truth; A is false and R (as a concept) is true.
• Both wrong: R is essentially correct about line loading adding inductance to meet the condition.

Common Pitfalls:

Memorizing an incorrect formula; confusing R/L = G/C with spurious rearrangements; forgetting that matching the ratio, not absolute values, yields distortionless propagation.

Final Answer:

A is wrong but R is correct