The maximum induced emf in a generator rotating at 210 rpm is 35 V . How fast must the rotor of

step 1 In this problem, we're going to talk about the electromotive force. So consider that we have a g

The maximum induced emf in a generator rotating at 210 rpm...

The maximum induced emf in a generator rotating at 210 $\mathrm{rpm}$ is 35 $\mathrm{V} .$ How fast must the rotor of the generator rotate if it is to generate a maximum induced emf of 55 $\mathrm{V}$ ?

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Key Concepts

Electromagnetic Induction

Electromagnetic induction is the process by which a time-varying magnetic field induces an electromotive force (emf) in a conductor. This phenomenon, formalized by Faraday's Law, is the fundamental principle behind the conversion of mechanical energy into electrical energy in generators.

AC Generator Operation

An AC generator converts mechanical energy into electrical energy by rotating a coil within a magnetic field. This rotation causes a continuously changing magnetic flux through the coil, which in turn produces an alternating current (AC) voltage. Understanding this mechanism is critical for analyzing and designing systems that produce AC power.

Proportionality Between Rotational Speed and Induced EMF

The magnitude of the induced emf in a generator is directly proportional to the rotational speed of its coil, assuming the magnetic field strength and coil properties remain constant. This proportionality implies that changes in the rotational speed lead to a corresponding change in the induced voltage, a concept often used when modifying generator outputs for specific applications.

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