(Solution) - Small single phase permanent magnet ac generators are frequently -(2025 Original AI-Free Solution)

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Small single-phase permanent-magnet ac generators are frequently used to generate the power for lights on bicycles. For this application, these generators are typically designed with a significant amount of leakage inductance in their armature winding. A simple model for these generators is an ac voltage source ea(t) = wKa cos cot in series with the armature leakage inductance La and the armature resistance Ra. Here co is the electrical frequency of the generated voltage which is determined by the speed of the generator as it rubs against the bicycle wheel. Assuming that the generator is running a light bulb which can be modeled as a resistance Rb, write an expression for the minimum frequency w min which must be achieved in order to insure that the light operates at constant brightness, independent of the speed of the bicycle.