Question

The rotating loop in an AC generator is a square 14.0 cm on a side. It is rotated at 40.0 Hz in a uniform field of 0.800 1. Calculate the following quantities as functions of time t, where is in seconds (a) the flux through the loop (b) the emf induced in the loop (c) the current induced in the loop for a boop resistance of 1.500 Id) the power delivered to the loop w (e) the torque that must be exerted to rotate the loop

Answer 1

flux through the loop will be given by

flux = B*A

B = 0.800 T

Ax = A*cos wt

w = 2*pi*f

w = 2*pi*40.0 = 251.3

Ax = side^2*cos wt = 0.14*0.14*cos (251.3*t) = 0.0196*cos (251.3*t) m^2

flux = 0.0196*0.800*cos (251.3*t) = 0.01568*cos (251.3*t) T.m^2

flux = 15.68*cos (251.3*t) mT-m^2

B.

EMF = N*A*B*w*sin wt

N = 1

EMF = 1*0.0196*0.800*251.3*sin (251.3*t)

EMF = 3.94*sin (251.3*t) V

C.

i = EMF/R

i = (3.94/1.50)*sin (251.3*t)

I = 2.63*sin (251.3*t)

D.

Power = EMF*i = 3.94*2.63*(sin (251.3*t))^2

P = 10.36*(sin (251.3*t))^2 W = 10.36*(sin²(251.3*t)) W

E.

torque = i*A*B*sin wt

torque = 2.63*0.0196*0.800*sin (251.3*t)*sin (251.3*t) = 0.0412*(sin (251.3*t))^2

torque = 41.2*(sin (251.3*t))^2 mN-m = 41.2*sin²(251.3*t) mN-m

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