Alternating EMF is given by

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E=E_msinθ

Explanation: An alternating electromotive force (EMF) is a voltage that changes its magnitude and direction periodically. The standard mathematical expression representing this sinusoidal variation over time or angular position is $E = E_m \sin heta$. Working Principle: When a coil rotates in a uniform magnetic field with angular velocity $\omega$, the magnetic flux linked with the coil varies as $\Phi = \Phi_m \cos(\omega t)$. According to Faraday's law of electromagnetic induction, $e = -\frac{d\Phi}{dt}$, leading to a sinusoidal induced EMF. At any instant, the instantaneous value $E$ is determined by the projection of the maximum EMF $E_m$ onto the vertical axis, represented by the sine function of the rotation angle $ heta = \omega t$. Key Formulas: $E = E_m \sin heta$ — Instantaneous EMF equation; $ heta = \omega t = 2\pi f t$ — Angular relationship Key Points: The sine function is the standard reference for AC waveforms.; $E_m$ represents the peak amplitude of the voltage.; $ heta$ is the phase angle in radians or degrees at any specific instant.; The wave repeats its cycle every $2\pi$ radians. Advantages: Mathematical simplicity for circuit analysis; Aligned with standard phasor diagram representation Disadvantages: Does not account for non-sinusoidal harmonics; Assumes an ideal uniform magnetic field Applications: AC generator modeling; Power system frequency analysis Additional Info: The cosine function $E = E_m \cos heta$ is merely a phase-shifted version of the sine wave ($90^\circ$ lead).. Option B represents a DC constant value.. Option D is not a physical representation of an EMF waveform. Answer: A is correct — The alternating EMF is defined by the sinusoidal function $E = E_m \sin heta$, representing the periodic change in voltage over an angle $ heta$. Exam Tip: Remember that in phasors, a sine wave is represented at angle $0^\circ$ (horizontal reference), while cosine starts at the peak.

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