The system below is intended to provide a source of electric light during power

Question

The system below is intended to provide a source of electric light during power outages: when the power fails, the weight is released, rotating the shaft of the motor, which acts as a generator. The motor is a permanent magnet DC motor with an armature resistance of 2 omega and a no-load speed of 1200 rpm when connected to a 12 V battery. The light bulb has a resistance of 8 omega. The moment of inertia of the rotating components, as well as the friction in the bearings, is negligible. (a) Sketch the voltage v(t) following the release of the weight. (b) What fraction of the potential energy of the weight is delivered to the light bulb?

Explanation / Answer

v(t) has a maximum value of 0.85 meters above ground;

43.35% of the potential energy of the weight is converted to light bulb;

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