Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 33 of 127
What is the formula for the inductive reactance \(X_L\) of an inductor of inductance \(L\) connected to an AC source of frequency \(f\)?
A
\(X_L = \frac{1}{2\pi f L}\)
B
\(X_L = 2\pi f L\)
C
\(X_L = 2\pi f / L\)
D
\(X_L = L / (2\pi f)\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \(X_L = 2\pi f L\)
Concept:

Inductive reactance \(X_L\) is the opposition offered by an inductor to the flow of alternating current, expressed in ohms (\(\Omega\)).

Formula / Reaction:

$$X_L = \omega L = 2\pi f L$$

Solution:

  • Induced back emf is \(v = L \frac{di}{dt}\). For \(i = I_0 \sin(\omega t)\), \(v = \omega L I_0 \cos(\omega t)\).


  • Peak voltage is \(V_0 = \omega L I_0\).


  • Therefore, inductive reactance is \(X_L = \frac{V_0}{I_0} = \omega L = 2\pi f L\).


Why other options are incorrect:

  • Opt_A: This is the formula for capacitive reactance \(X_C\).


  • Opt_C: Inverts the placement of inductance.


  • Opt_D: Inverts the placement of frequency.

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