Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

E=Emsinθ

Quick Summary: 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 $E = E_m \sin \theta$.

💡 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 $E = E_m \sin \theta$ .

🔢 Key Formulas

$E = E_m \sin \theta$ — Instantaneous EMF equation

$\theta = \omega t = 2\pi f t$ — Angular relationship

⚙️ 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 $\theta = \omega t$ .

📌 Key Points

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The sine function is the standard reference for AC waveforms.
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$E_m$ represents the peak amplitude of the voltage.
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$\theta$ is the phase angle in radians or degrees at any specific instant.
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The wave repeats its cycle every $2\pi$ radians.

✅ Advantages

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Mathematical simplicity for circuit analysis
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Aligned with standard phasor diagram representation

❌ Disadvantages / Limitations

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Does not account for non-sinusoidal harmonics
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Assumes an ideal uniform magnetic field

🛠️ Applications / Uses

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AC generator modeling
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Power system frequency analysis

📄 Additional Information

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The cosine function $E = E_m \cos \theta$ is merely a phase-shifted version of the sine wave ( $90°$ lead).
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Option B represents a DC constant value.
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Option D is not a physical representation of an EMF waveform.

📊 Diagram / Illustration

✅

A is correct — The alternating EMF is defined by the sinusoidal function $E = E_m \sin \theta$ , representing the periodic change in voltage over an angle $\theta$ .

Core Concepts Used

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Electromagnetic Induction Sinusoidal Waveforms AC Fundamentals

💡 EXAM TIP

Remember that in phasors, a sine wave is represented at angle $0°$ (horizontal reference), while cosine starts at the peak.

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