The armature of a simple ac generator has 10 circular loops of wire, each with a

Question

The armature of a simple ac generator has 10 circular loops of wire, each with a radius of 10 cm. It is rotated with a frequency of 60 Hz in a uniform magnetic field of 900mT. What is the maximum emf induced in the loops? Express your answer using two significant figures. How often is this value attained? Express your answer using two significant figures. The armature of a simple ac generator has 10 circular loops of wire, each with a radius of 10 cm. It is rotated with a frequency of 60 Hz in a uniform magnetic field of 900mT. How often is this value attained? Express your answer using two significant figures. If the time period in part B were cut in half, what would be the new maximum emf value? Express your answer using two significant figures.

Explanation / Answer

Area of a circular loop

A=pi*r2=pi*0.12=0.0314 m2

angular frequency

W=2pif =2pi*60=377 rad/s

a)

Maximum emf induced

Eo=NBAW =10*0.0314*(900*10-3)*377

Eo=106.54 Volts

b)

Time period

T=1/f =1/60 =0.01667 sec

peak value is attained for every half of the time period i.e T/2

t=T/2 =8.3*10-3 s

c)

given

T=0.01667/2=8.3*10-3 s

angular frequency

W=2pi/T=2pi/(8.3*10-3)=754 rad/s

Maximum induced emf

Eo=10*(900*10-3)*0.0314*754

Eo=213.1 Volts

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