40-turn rectangular coil with dimensions 0.13 m 0.35 m rotates in a uniform magn

Question

40-turn rectangular coil with dimensions 0.13 m 0.35 m rotates in a uniform magnetic field of magnitude 0.55 T at 3,300 rev/min. (Use the following as necessary: t. Do not use other variables, ubstitute numerical values. Assume t is in seconds.) (a) Determine the emf induced in the coil as a function of time. (Assume the plane of the coil is perpendicular to the magnetic field at t O. Further, assume & is in volts.) E(t)- (b) If the coll is connected to a 1,000 resistor, what is the power as a ranction of time required to keep the col tunning at 3,300 rpm? (Assume p is in watts.) (c) Answer part (b) if the coil is connected to a 2,000 resistor

Explanation / Answer

A = area of coil = 0.13*0.35 m^2 = 0.0455 m^2

number of turns N = 40

magnetic field B = 0.55 T

angular frequency w( omega) = 3300 rev/min = 3300*2pi/60 = 345.6 radd/s

(a)

magnetic flux = N*B*A*cos(wt)

induced emf = -rate of change in flux

e(t) = -N*B*A*(d/dt)*(coswt)

e(t) = w*N*B*A*sin(wt)

e(t) = 345.6*40*0.55*0.0455*sin(345.6t)

e(t) = 346sin(345.6t)    v

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(b)

power dissipated = e^2/R = (346*sin(345.6t))^2/1000

P = 120*(sin(345.6t))^2   W

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(c)

power = e^2/R = (346*sin(345.6t))^2/2000

P = 60*(sin(345.6t))^2 W

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