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A transmission line is excited by a 100 V DC source. If the reflection coefficients at both ends are 1, what will happen to the oscillations on the line?

Difficulty: Hard

Correct Answer: the oscillations will continue indefinitely

Explanation:


Introduction / Context:
Transmission line theory considers wave reflections at mismatched terminations. Reflection coefficients determine how much energy is reflected back, influencing standing waves and oscillations.


Given Data / Assumptions:

  • DC source = 100 V applied.
  • Reflection coefficient at both ends = 1 (perfect reflection).


Concept / Approach:
If both ends reflect 100% of the energy, no dissipation occurs. The wave will bounce indefinitely, sustaining oscillations unless loss mechanisms are introduced.


Step-by-Step Solution:

Reflection coefficient Γ = +1 means full constructive reflection.At source end and load end, energy reflects back entirely.Thus, energy is trapped → oscillations never decay.


Verification / Alternative check:
In practical systems, even small losses attenuate oscillations. But with ideal assumption (Γ = 1 at both ends), oscillations persist forever.


Why Other Options Are Wrong:

No oscillations: incorrect, reflection ensures oscillations.1 or 2: wrong, indefinite reflection occurs.Finite oscillations: contradicts perfect reflection assumption.


Common Pitfalls:

Forgetting that Γ = 1 means no energy is absorbed by load/source.


Final Answer:

the oscillations will continue indefinitely
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