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Question #92931

Difficulty: 5/10 | 🟢 Free

The Question

A generator coil of self-inductance $L$ , total resistance $R$ , and $N$ turns each of area $A$ is placed in a uniform magnetic field $B$ . At $t=0$ , the coil is at rest with its area vector parallel to the magnetic field. It is then subjected to a constant angular acceleration $\alpha$ . Let $\Phi_0 = NAB$ be the maximum flux. Which of the following expressions gives the leading-order term for the instantaneous induced current $i(t)$ in the coil for infinitesimally small times ( $t \to 0$ )? (Assume the external circuit is closed and has no additional components).

Options

A.
$\frac{\Phi_0 \alpha^2 t^4}{8L}$
B.
$\frac{\Phi_0 \alpha^2 t^3}{2R}$
C.
$\frac{\Phi_0 \alpha t^2}{2L}$
D.
$\frac{\Phi_0 \alpha^2 t^4}{4L}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

AC Generator Back-EMF|Phasor Rotation Convention|Average vs. Instantaneous Calculus

Why This Question Is Tricky

Examiner Levers

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Common Mistakes

This problem tests the breakdown of steady-state AC phasor analysis during transient electromechanical startup.

Students often incorrectly apply Ohm's Law or fixed reactance formulas to the instantaneous back-EMF, leading to $i \approx \mathcal{E}(t)/R$ (Option B) or $i \approx \mathcal{E}(t)/(\omega L)$ (Option C).

This trap exploits the cognitive dissonance between steady-state AC theory and time-domain differential equations.

By failing to recognize that the initial condition $i(0)=0$ forces the $L \frac{di}{dt}$ term to dominate the $R i$ term at infinitesimally small times, students bypass the necessary integration of the transient differential equation.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Induction - Class 12
Concept	AC Generator Back-EMF
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free