In a model AC generator, a 499 turnrectangular coil 9.0 cm by28 cm rotates at 11

Question

In a model AC generator, a 499 turnrectangular coil 9.0 cm by28 cm rotates at 116 rev/min in a uniform magnetic field of0.57 T. (a) What is the maximum emf induced in thecoil?
1 V
(b) What is the instantaneous value of the emf in the coil att = (/38) s?Assume that the emf is zero at t = 0.
2 V
(c) What is the smallest value of t for which the emf willhave its maximum value?
3 s (a) What is the maximum emf induced in thecoil?
1 V
(b) What is the instantaneous value of the emf in the coil att = (/38) s?Assume that the emf is zero at t = 0.
2 V
(c) What is the smallest value of t for which the emf willhave its maximum value?
3 s

Explanation / Answer

Induced emf E = N sin t                        = NBA sin [ ( 2 / T )t ]      ----- ( 1) (a). maximum induced emf = N BA where N = No.of truns = 499            = 116 rev / min               = 116 * 2 rad / 60 s               = 12.147 rad / s            B= magnetic field = 0.57 T            A= area = 9 cm * 28 cm               = 252 cm ^ 2               = 252 * 10 ^ -4 m ^ 2 substitue values we get maximum induced emf = 87.06 V (b). substitue t = / 38 in eq ( 1 ) we get E =NBA sin [ ( / 38 ) ]                                                                     = 87.06 * sin 1.00423                                                                    =87.06 *0.8437                                                                   = 73.456 V (c)If sin [ t ]  =1 then emf is maximum. from this t = / 2                 t = / ( 2 * )                   = 0.1293 s

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