Anemometers (pictured) are used to measure wind speeds. Wind striking the cups c

Question

Anemometers (pictured) are used to measure wind speeds. Wind striking the cups causes the assembly to rotate; a gauge measures the frequency of this rotation and translates the data into wind speed. The length of each arm, as measured from cup to cup, is 0.445 m. The friction in the bearings is negligible, so the tangential speed of the cups matches the wind speed fairly closely. Your company makes anemometers and plans to install light bulbs on them for high wind warnings. The idea is to attach a coil of wire of radius 0.132 m to one of the arms and use the EMF induced by the magnetic field of the Earth to light the bulb. The bulbs possess 234 Ohm of internal resistance but need 12.5 W of rms power dissipation to be visible at night. (The resistance of the wire is negligible.) Although company management wants this new feature, you have doubts about its practicality. Assuming the magnetic field of the Earth is 0.500 times 10^-4 T and is oriented roughly horizontal with the Earth, and that 41.8 m/s (93.5 mph) is considered the threshold of dangerous wind speed, calculate the number of turns in the coil wire needed to light the bulb.

Explanation / Answer

Let the number of turn be N

Emf induced in rotating coil is V=NABw

Where A is area of coil,w=v/r

Power of bulb=12.5

R=234 ohm

So V=sqrt(12.5*234)=54.08

So N=62401 turns approx

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