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For an inductor in AC analysis, how does inductive reactance vary with the operating frequency of the applied sinusoidal voltage?

Difficulty: Easy

Correct Answer: inductive reactance increases with operating frequency

Explanation:


Introduction / Context:
Inductive reactance captures how an inductor resists changes in current when excited by alternating current. Understanding its dependence on frequency is crucial for filter design, impedance matching, and transient response prediction.


Given Data / Assumptions:

  • Sine-wave excitation (steady-state AC).
  • Ideal inductor model.
  • Angular frequency relation omega = 2 * pi * f.


Concept / Approach:
The formula for inductive reactance is X_L = 2 * pi * f * L. This shows a direct proportionality: doubling frequency doubles X_L. At dc (f = 0), X_L = 0, meaning the inductor behaves like a short in steady state for pure dc.


Step-by-Step Solution:

1) Use X_L = 2 * pi * f * L.2) Observe that X_L is proportional to f.3) Conclude that as f increases, X_L increases linearly.


Verification / Alternative check:
At dc, X_L = 0, confirming option B is false and reinforcing the proportional trend with frequency for nonzero f.


Why Other Options Are Wrong:

Decreases with frequency: Opposite of the formula’s prediction.Maximum at dc: Incorrect; it is zero at dc.No relationship: There is a clear linear relationship.None of the above: Option stating increase with frequency is correct.


Common Pitfalls:
Confusing capacitive reactance, which decreases with frequency, with inductive reactance, which increases.


Final Answer:
inductive reactance increases with operating frequency.

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