Frequency of a simple generator: A conductive loop on the rotor of a simple two-pole, single-phase generator turns at 400 revolutions per second (rps). What is the frequency of the induced output voltage?

Introduction / Context:
In rotating electric machines, electrical frequency depends on mechanical speed and the number of magnetic poles. Understanding this relationship is crucial for generators, alternators, and synchronous machines, linking mechanical rotation to AC frequency output.

Given Data / Assumptions:

• Two-pole (P = 2), single-phase generator.
• Mechanical speed n = 400 rps.
• Standard relation: f = (P/2) * n for frequency in hertz.

Concept / Approach:
Each mechanical revolution produces one electrical cycle per pole pair. With P = 2 (one pole pair), the electrical frequency equals the mechanical rotation rate directly.

Step-by-Step Solution:

Verification / Alternative check:
For a four-pole machine (two pole pairs) at the same speed, frequency would be 800 Hz, showing proportionality to P/2 and confirming the formula used here.

Why Other Options Are Wrong:

• 40 Hz or 100 Hz: These would correspond to much slower speeds or different pole counts.
• indeterminable: Not the case; speed and pole count are sufficient to determine f.

Common Pitfalls:

• Using rpm without converting to rps; here rps is already provided, simplifying the calculation.

Final Answer:
400 Hz