A generator consists of 800 turns of wire with each turn a square loop of side 4

Question

A generator consists of 800 turns of wire with each turn a square loop of side 40 centimeters. The maximum magnetic field averaged over a loop is 0.50 T and each loop has a resistance of 0.05 Ohms. If the loops are spinning at a constant angular velocity of 60 revolutions per second what is the

(A) Peak and RMS EMF?

(B) Peak and RMS current?

(C) Magnetic moment of the loops?

(D) Torque on the loops?

(E) Determine the direction sense of the induced current when the loop is in the plane of this page (flux is zero) and the angular velocity is to the right with magnetic field directed towards the top of the page? (Sketch loop, velocity vector, magnetic field and current sense). (F) What is the direction of the torque on the loop in part (E)?

Explanation / Answer

A)
w = 60 rps = 60 x 2pi rad / s = 120pi rad/s

Maximum Induced emf = NABw

= (800) x ( 0.40 x 0.40 m^2 ) x (0.50 T) x (120 pi )

= 24127.4 Volt

RMS emf = Emax / sqrt(2) = 24127.4 / 1.414 = 17060.65 Volt

B) Ipeak = Emax / R

and R = 0.05 x 800 = 40 ohm

Ipeak = 24127.4 / 40 = 603.2 A ........Ans

Irms = Erms / R = 17060.65 / 40 = 426.5 A .......Ans

C) moment of loops = NIA

I = Ipeak sin(wt) = 603.2 sin(120 pi t)

moment = 800 x (603.2 sin(120 pi t) x 0.40 x0.40) = 77209.6 sin(120pi t) A m^2

Maximum moment = 77209.6 A m^2

Rms = 54595.4 A m^2

d) torque = moment x B =

= 77209.6 sin(120pi t) x 0.5 = 38604.8 sin(120 pi t) N m

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