Question

A generator consists of a 12-cm by 16-cmrectangular loop with 500 turns of wire spinning at 60 Hz in a 25 mT uniform magnetic field. The generator output is connected to a series RCcircuit consisting of a 150 ? and a 35 ?F capacitor.

1)What is the average power delivered to the circuit?

Answer 1

From the given data

A = 0.12*0.16

= 0.0192 m^2

N = 500 turns

f = 60 Hz

angular frequency, w = 2*pi*f

= 2*pi*60

= 377 radians

B = 25 mT = 25*10^-3 T

maximum induced emf = N*A*B*w

= 500*0.0192*25*10^-3*377

= 90.5 V

capacitive reactance, XC = 1/(w*C)

= 1/(377*35*10^-6)

= 75.8 ohms

impedance of the circuit, z = sqrt(R^2 + Xc^2)

= sqrt(150^2 + 75.8^2)

= 168 ohms

maximum current through the circuit, Imax = Vmax/z

= 90.5/168

= 0.539 A

the average power delivered to the circuit, P_avg = Imax^2*R/2

= 0.539^2*150/2

= 21.8 W <<<<<<<-------------------Answer