What happens to the inductive reactance when the frequency of the ac supply is increased?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → It increases.
The inductive reactance is \( X_L=\omega L \), with \( \omega=2\pi\nu \). For a given inductor it is directly proportional to the frequency.
Option (1) It increases. — Correct. At a higher frequency the current changes faster. So the self-induced emf that opposes it is larger, and \( X_L=2\pi\nu L \) grows in proportion to \( \nu \).
Option (2) It decreases. — Incorrect. The capacitive reactance \( X_C=1/\omega C \) falls as the frequency rises. The inductive reactance does the opposite.
Option (3) It remains the same. — Incorrect. The resistance of a resistor is the same at every frequency, but the inductive reactance changes in proportion to \( \omega \).
Option (4) It decreases inversely. — Incorrect. The inductive reactance is directly proportional to the frequency. The inverse dependence \( 1/\omega C \) belongs to a capacitor.
NCERT (2026-27):
AC Voltage Applied to an Inductor – “… The quantity ωL is analogous to the resistance and is called inductive reactance, denoted by XL:
\( X_L=\omega L \qquad (7.13) \)
… The inductive reactance is directly proportional to the inductance and to the frequency of the current.”