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.
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ABoth A and R are correct and R is the correct explanation of A
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BBoth A and R are correct but R is not the correct explanation of A
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CA is correct but R is wrong
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DA is wrong but R is correct
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EBoth A and R are wrong
Answer
Correct Answer: A is wrong but R is correct
Explanation
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:
1) State the correct condition: R/L = G/C.2) Rearranging gives L/C = R/G, but not L = (R * C) / G.3) Therefore, the assertion L = (R * C) / G is dimensionally and conceptually incorrect.4) Line loading (historically adding series inductance, e.g., loading coils) increases L so that R/L approaches G/C, thereby reducing distortion on low-loss lines where G is small.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