A student connects a small lamp in series with a coil to an a.c. mains supply. Initially the lamp glows with normal brightness. When she slowly slides an iron rod halfway into the coil, she observes that
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → The lamp glows dimmer because the coil’s opposition to current increases.
An iron rod inside the coil greatly increases its self-inductance \( L \), because iron has a large permeability. The coil’s opposition to a.c. is its impedance:
\( X_{L} = \omega L,\quad Z = \sqrt{R^{2} + X_{L}^{2}} \)
As \( L \) rises, \( X_{L} \) and \( Z \) rise, so the current \( I = V/Z \) falls and the lamp glows dimmer. The resistance of the coil wire does not change.
Option (1) The lamp glows brighter because the coil’s resistance increases. — Incorrect. A larger opposition would make the lamp dimmer, not brighter. Besides, the resistance of the wire is unchanged; it is the reactance that increases.
Option (2) The lamp glows dimmer because the coil’s opposition to current increases. — Correct. The inductive reactance \( \omega L \) increases.
Option (3) The lamp glows brighter because self-inductance of coil decreases. — Incorrect. An iron core increases \( L \); it does not decrease it.
Option (4) The brightness remains unchanged because the a.c. voltage is constant — Incorrect. The current depends on the impedance as well as on the voltage.
NCERT (2026-27):
AC Voltage Applied to a Capacitor – “… The switch is closed and after sometime, an iron rod is inserted into the interior of the inductor. The glow of the light bulb (a) increases; (b) decreases; (c) is unchanged, as the iron rod is inserted. Give your answer with reasons. … Hence, the inductance of the coil increases. Consequently, the inductive reactance of the coil increases. As a result, a larger fraction of the applied ac voltage appears across the inductor, leaving less voltage across the bulb. Therefore, the glow of the light bulb decreases.”