Question

Whenever a magnet is moved either towards or away from a conducting coil, an emf is induced whose magnitude is independent of the:

• A. number of turns in the coil
• B. resistance of the coil
• C. speed with which the magnet is moved
• D. area of the coil

Hint:

Induced emf is \(N\,d\Phi/dt\), so it depends on turns, speed and area. Resistance only decides the current, not the emf.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Faraday law of induction: the emf induced in a coil is \(\varepsilon = -N \dfrac{d\Phi}{dt}\), where \(N\) is the number of turns and \(\Phi\) is the flux through one turn.

Step 2: What the emf depends on:
Flux is \(\Phi = BA\cos\theta\). A larger area \(A\) gives more flux, so the emf depends on the area.
A faster magnet changes the flux faster, so the emf depends on the speed.
The emf is multiplied by \(N\), so it depends on the number of turns.

Step 3: The role of resistance:
Resistance of the coil does not appear in the formula for the emf. It only decides the current, \(I = \varepsilon / R\). So the emf is independent of the resistance.

Step 4: Why the other options are wrong:
(A) number of turns: the emf is directly proportional to it. (C) speed: it changes \(d\Phi/dt\). (D) area: it changes the flux. So the emf does depend on all three.

Final Answer:
The induced emf is independent of the resistance of the coil. This is option (B). \[ \boxed{\text{(B) resistance of the coil}} \]