Physics Electromagnetic Induction UHS 2023
PMDC Verified Question 23 of 69
The expression for the emf produced by A.C generator is?
A
\( N \omega A B \sin(\theta) \)
B
\( N \omega A B \cos(\theta) \)
C
\( N \omega A B \)
D
\( N \omega A B \tan(\theta) \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( N \omega A B \sin(\theta) \)
Concept:

An AC generator rotates a coil of area \( A \) inside a uniform magnetic field \( B \) at a constant angular velocity \( \omega \).

Formula:

$$ \varepsilon = \varepsilon_0 \sin(\omega t) $$

Solution:

  • The flux through the coil is \( \phi = N A B \cos(\theta) \), where \( \theta = \omega t \).


  • Taking the time derivative (Faraday's law) yields a sine function: \( \varepsilon = - \frac{d\phi}{dt} = N A B \omega \sin(\omega t) \).


  • Since \( \omega t = \theta \), the standard expression is \( N \omega A B \sin(\theta) \).


Why other options are incorrect:

The cosine function represents the magnetic flux, not the derivative (EMF). Option C only gives peak EMF. The tangent function is never used in standard generator wave models.

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