Assertion (A): The velocity factor (VF) of a transmission line is the ratio of wave (phase) velocity on the line to the speed of light in vacuum. Reason (R): If the conductors are immersed in a non-magnetic insulating liquid (relative permittivity > 1), the wave velocity increases. Choose the correct option about A and R.
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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
Answer
Correct Answer: A is correct but R is wrong
Explanation
Introduction:Velocity factor describes how fast an electromagnetic wave propagates along a transmission line relative to light in vacuum. It depends primarily on the line's effective permittivity and permeability.
Given Data / Assumptions:
- Non-magnetic medium: mu_r ≈ 1
- Insulating liquid has epsilon_r > 1
- VF = v/c where v is phase velocity on the line
Concept / Approach:Phase velocity v = c / sqrt(epsilon_r * mu_r). For non-magnetic media, mu_r ≈ 1, so v ≈ c / sqrt(epsilon_r). Increasing epsilon_r decreases v, therefore VF decreases when immersed in a higher-permittivity dielectric.
Step-by-Step Solution:
1) A is a correct definition: VF = v / c.2) For epsilon_r > 1, v = c / sqrt(epsilon_r) < c.3) Hence immersing the line in such a liquid reduces, not increases, wave velocity.4) Therefore R is false.Verification / Alternative check:Typical coaxial cables with solid polyethylene (epsilon_r ≈ 2.25) have VF ≈ 0.66, confirming reduced velocity in higher-permittivity dielectrics.
Why Other Options Are Wrong:
- A/B: R is not true, so these cannot be correct.
- D: A is not wrong.
Common Pitfalls:Confusing refractive index effects; assuming any insulating medium increases speed.
Final Answer:A is correct but R is wrong