In a simple AC generator, as the armature passes the 270° position of rotation within a uniform magnetic field, what is the instantaneous polarity/magnitude of the induced voltage?

Introduction / Context:An elementary AC generator produces a sinusoidal voltage as the armature (or coil) rotates in a magnetic field. Understanding how the induced voltage relates to angular position helps visualize phase, polarity, and peak occurrences within a cycle.

Given Data / Assumptions:

• Uniform rotation with angular position measured from the zero-crossing reference where induced voltage follows a sine function.
• Ideal sinusoidal behavior: v(θ) ∝ sin(θ).
• Neglect effects like armature reaction and nonuniform fields.

Concept / Approach:If v(θ) is sinusoidal, then key angles are: 0° → 0 V, 90° → +Vmax, 180° → 0 V, 270° → −Vmax, and 360° → 0 V (completing the cycle). Thus, at 270°, the induced voltage reaches its most negative peak, indicating both maximum magnitude and negative polarity.

Step-by-Step Solution:Model: v(θ) = Vmax * sin(θ).Evaluate at θ = 270°: sin(270°) = sin(3π/2) = −1.Therefore, v(270°) = −Vmax, i.e., the maximum negative value.This corresponds to the coil plane and flux cutting rate aligning for maximum magnitude with negative sign based on the chosen reference.

Verification / Alternative check:Plotting one cycle of a sine wave or recalling standard unit circle values confirms the mapping of angles to peaks and zero crossings, validating the 270° result as −Vmax.

Why Other Options Are Wrong:

• Between maximum negative and zero / between zero and maximum positive: These describe intermediate magnitudes, not the peak at 270°.
• At maximum positive: Occurs at 90°, not 270°.
• Zero volts: Occurs at 0°, 180°, and 360°.

Common Pitfalls:

• Confusing mechanical position reference; ensure the sine reference starts at 0° = zero crossing.
• Mixing sine and cosine references; cosine would shift all angles by 90°.

Final Answer:at maximum negative