When a magnet is inserted into a coil, the induced e.m.f. in the coil…

The correct answer is Option (2) → the resistance of the coil.

By Faraday’s law, the induced emf equals the rate of change of the flux linked with the coil:

    \( \displaystyle \varepsilon = -N\,\frac{d\phi}{dt} \)

Anything that changes N or the rate of change of flux changes the emf. The resistance does not appear in this relation; it only decides the current, \( I = \varepsilon/R \).

Option (1) the number of turns in the coil. — Incorrect. The emf is proportional to the number of turns, since the same change of flux induces an emf in every turn.

Option (2) the resistance of the coil. — Correct. Changing the resistance of the coil changes the induced current but not the induced emf.

Option (3) the magnetic moment of the magnet. — Incorrect. A magnet of larger magnetic moment produces a stronger field, so the flux through the coil, and its rate of change, are larger.

Option (4) the speed of the magnet. — Incorrect. A faster magnet changes the flux more quickly, so the emf is larger.

Note: A similar question was also asked in CUET (UG) 2025 on 02-06-2025 (Slot 1).

NCERT (2026-27):
Faraday’s Law of Induction – “… The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit. Mathematically, the induced emf is given by

    \( \displaystyle \varepsilon = -\frac{d\Phi_B}{dt} \qquad (6.3) \)

… In the case of a closely wound coil of N turns, change of flux associated with each turn, is the same. Therefore, the expression for the total induced emf is given by

    \( \displaystyle \varepsilon = -N\frac{d\Phi_B}{dt} \qquad (6.4) \)

The induced emf can be increased by increasing the number of turns N of a closed coil.”