Your friend decides to generate electrical power by rotating a 100,000 turn coil

Question

Your friend decides to generate electrical power by rotating a 100,000 turn coil of wire around an axis in the plane of the coil and through its center. The coil is perpendicular to Earth's magnetic field in a region where the field strength is equal to 0.300 G. The loops of the coil have a radius of 18.0 cm, and the coil has negligible resistance.

(a) If your friend turns the coil at a rate of 140 rev/s, what peak current will exist in a 1600 resistor that is connected across the terminals of the coil?
mA

(b) The average of the square of the current will equal half of the square of the peak current. What will be the average power delivered to the resistor?
W

Explanation / Answer

a)

Peak Induced emf is given by

EP=NBAW=(100000)*(0.3*10-4)(pi*0.182)(140*2pi)

EP=268.6 Volts

Peak Current

IP=EP/R=268.6/1600 =0.168 A=168 mA

b)

Rms Current

Irms=0.168/sqrt(2)=0.1187 A

Average power

Pavg=Irms2R=0.11872*1600

Pavg=22.55 W

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