The Tacoma electrical power plant (located just up the valley) has a generator t

Question

The Tacoma electrical power plant (located just up the valley) has a generator that is represented by the picture below. The loop (which is 0.6 m high by 1.5 m wide with N = 500 turns) spins such that the magnetic flux through the loop is given by phi_B (t) = NBA sin (omega t). The coil turns in a magnetic field of 0.4 T, and spins at an angular frequency of oemga = 62.8 rad/s. What is the maximum EMF (epsilon) induced in the coil? (If you cannot get an answer, use a value of 1500 with appropriate units for later parts of the problem.) If the coil is connected to a resistive load of R = 300 Ohm, what is the maximum current that will flow in the resistor? (If you cannot get an answer, use a value of 4700 with appropriate units for later parts of the problem.) What is the magnitude of the maximum torque exerted on the loop due to the induced current?

Explanation / Answer

a)

B = magnetic field = 0.4 T

w = angular frequency = 62.8 rad/s

A = Area = 0.6 x 1.5 = 0.9 m2

N = number of turns = 500

Maximum EMF is given as

E = NBAw

E = 500 x 0.4 x 0.9 x 62.8 = 11304 volts

b)

R = resistance = 300 ohm

i = current = induced EMF / R = 11304 / 300 = 37.7 A

c)

maximum torque = NiAB = 500 x 37.7 x 0.4 x 0.9 = 6786

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