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In a purely inductive circuit, what happens to the inductive reactance and the current if the frequency is halved?

Asked in JEE Main 17th March 2nd Shift 2021 · Reactance and frequency

(1) reactance halved and current doubled
(2) reactance doubled and current halved
(3) both reactance and current doubled
(4) both reactance and current halved

Answer: (1) reactance halved and current doubled

Step-by-step solution

X_L=ω L∝ f, so halving the frequency halves X_L.

I=V/(X_L), so a halved reactance doubles the current.

Why the other options are wrong

(2) Inverts the frequency dependence of X_L.
(3) The current cannot rise with the reactance.
(4) Lower reactance means larger, not smaller, current.

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