In the tuning circuit of a radio, a particular station is selected by…

The correct answer is Option (3) → the capacitance of a capacitor in the circuit

The tuning circuit of a radio is a resonant circuit. A station is received best when the resonant frequency \( \omega_0=1/\sqrt{LC} \) of the circuit matches the frequency of its signal.

Option (1) the resistance of the circuit — Incorrect. The resistance does not appear in \( \omega_0=1/\sqrt{LC} \). It changes the height of the current peak but not the frequency at which the peak occurs.

Option (2) the strength of the signal received by the antenna — Incorrect. A stronger or weaker signal only changes the size of the current. The resonant frequency of the circuit stays the same.

Option (3) the capacitance of a capacitor in the circuit — Correct. A change in \( C \) changes \( \omega_0 \). When \( \omega_0 \) becomes nearly equal to the frequency of the wanted station, the current at that frequency is the largest.

Option (4) the frequency of the signal sent out by the station — Incorrect. Each station sends out its own fixed frequency. The listener cannot change it, so the circuit is changed to match it.

NCERT (2026-27):
AC Voltage Applied to a Series LCR Circuit – “… But to hear one particular radio station, we tune the radio. In tuning, we vary the capacitance of a capacitor in the tuning circuit such that the resonant frequency of the circuit becomes nearly equal to the frequency of the radio signal received.”