A combustion engine powers a generator The generator creates

A combustion engine powers a generator. The generator creates a current by using a drive shaft to rotate a stack of 200 coils in a uniform magnetic field. Each coil is a rectangle with width 10 cm and height 8 cm. The coil stack has a self-inductance of 3.42 mH and a resistance of 5 ohms. At what angular frequency should the coil stack be rotated such that the current produced has a 60 Hz frequency? If the rms voltage output of the coil stack is to be A 20 V, what is the magnitude of the magnetic field? What constant torque should the driveshaft provide?

Solution

A) angular frequency = 2 pi f

w = 2 xpi x 60 = 377 rad/s

b) Induced emf _rms   = N A B w

120 = 200 x (0.10 x 0.08) x B x 377

B = 0.2 T

c) torque = N I A B w

I = Vrms / R = 120 / 5 = 24 A

torque = 200 x 24 x (0.10 x 0.08) x 0.2 x 377

        = 2895.36 N m