High-Frequency Line Parameters: Inductive Reactance vs AC Resistance Assertion (A): At high frequencies, the line's inductive reactance is very large compared to its ac resistance. Reason (R): Due to skin effect, the ac resistance of a conductor is higher than its dc resistance.
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ABoth A and R are correct and R is correct explanation of A
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BBoth A and R are correct but R is not 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: Both A and R are correct but R is not correct explanation of A
Explanation
Introduction / Context:Distributed-parameter lines exhibit frequency-dependent reactance and resistance. This item tests understanding of how inductive reactance and skin-effect resistance scale with frequency and whether one explains the other.
Given Data / Assumptions:
- Inductance per unit length L is approximately constant with frequency over a wide range.
- Inductive reactance X_L = ω * L increases linearly with frequency.
- AC resistance R_ac rises with frequency due to skin effect.
Concept / Approach:
At high frequencies, X_L commonly exceeds R_ac, so the line is more inductive than resistive. Skin effect makes R_ac > R_dc, but that fact does not cause X_L to be large; rather, X_L is large because ω is large. Thus A is true, R is true, but R does not explain A.
Step-by-Step Solution:
1) Evaluate A: With increasing frequency, X_L = ωL grows, and typically X_L ≫ R_ac for RF conductors.2) Evaluate R: Skin depth decreases with frequency, shrinking effective cross-section and raising R_ac versus R_dc, so R is true.3) Causality check: The largeness of X_L is due to ωL, not because R_ac increased; hence R does not explain A.Verification / Alternative check:
Measurements on coax or twin-lead at RF show reactance dominating series resistance in many bands, despite rising R_ac.
Why Other Options Are Wrong:
Option A: Incorrect causal link. Option C/D/E conflict with correctness of A and R.
Common Pitfalls:
Attributing frequency behavior of reactance to resistive mechanisms; ignoring that both R_ac and X_L increase with frequency but for different physical reasons.
Final Answer:
Both A and R are correct but R is not correct explanation of A