Question

When a magnet is inserted into a coil, the induced e.m.f. in the coil does not depend on

• A. the number of turns in the coil.
• B. the resistance of the coil.
• C. the magnetic moment of the magnet.
• D. the speed of the magnet.

Hint:

Remember: \[ e=-N\frac{d\Phi}{dt} \] Induced e.m.f. depends on the rate of change of magnetic flux. Resistance affects the induced current, not the induced e.m.f.

Answer 1

The Correct Option is B

Concept: According to Faraday's law of electromagnetic induction, \[ e=-N\frac{d\Phi}{dt} \] where \[ e=\text{induced e.m.f.} \] \[ N=\text{number of turns of the coil} \] \[ \Phi=\text{magnetic flux} \] Thus, induced e.m.f. depends upon the rate of change of magnetic flux linked with the coil.

Step 1:Analyse the dependence on number of turns. From Faraday's law, \[ e\propto N \] Hence, induced e.m.f. depends on the number of turns.

Step 2: Analyse the dependence on magnetic moment. A stronger magnet produces a larger magnetic field and therefore a greater change in magnetic flux. Hence, induced e.m.f. depends on the magnetic moment of the magnet.

Step 3: Analyse the dependence on speed of the magnet. A faster moving magnet changes the magnetic flux more rapidly. Therefore, \[ \frac{d\Phi}{dt} \] increases and the induced e.m.f. increases. Hence, induced e.m.f. depends on the speed of the magnet.

Step 4: Analyse the dependence on resistance. The expression \[ e=-N\frac{d\Phi}{dt} \] contains no term involving resistance. Resistance affects the induced current, \[ I=\frac{e}{R} \] but not the induced e.m.f.

Step 5: State the answer. \[ { \begin{array}{c} \text{Induced e.m.f. does not depend on the resistance of the coil.} \end{array} } \] Hence, the correct option is \[ {(B)} \]