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Induced emf Developed torque Magnetization curve SEE 3433 ELECTRICAL MACHINES

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Induced emf Regardless of operation, emf is always induced in armature circuit when there is rotation Induced emf e a = B v l For a conductor of length l, moving at a speed v in magnetic field intensity B, the induced voltage is given by: e a = B v l X X X X v +ea+ea

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Induced emf

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l

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e a = 2 B m r l + e a In terms of flux per pole, where = B A and l + + _ _ + e a

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Induced emf where = B A and which gives This is an induced voltage for a single turn. If there are N turns with a parallel path,

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Developed torque Force produced, F = B l i For a conductor of length l, carrying current i in magnetic field intensity B, the torque developed is given by: F c = B i l X X X X F i

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Developed torque

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x l i i

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x l IaIa IaIa T = F r T c = B l I a r T 2c = 2 B l I a r In terms of flux per pole, where = B A and

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Developed torque This is torque for a single turn. If there are N turns with a parallel path, Similar to the constant obtained in induced emf !

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Magnetization curve Is a plot of the induced emf vs I f on an open armature circuit, at a given rotor speed +Ea+Ea I f Field current Induced emf E a = K (flux per pole) depends on field (stator) current and hence MMF of the stator circuit K is a constant – depends on physical construction of the machine - angular speed of the rotor At a given speed and K, the emf induced depends on Field circuit Armature circuit

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How does vary with the field current? Flux path produced by field: stator core air gap rotor core airgap stator core At low , core reluctance is small – most of MMF drop appear across air gap – consequently relation between and field current is almost linear (due to the airgap) IfIf Flux will increase with field current - but not necessarily linear! Magnetization curve

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How does vary with the field current? As field current increases, so too - some part of the core (especially the rotor teeth) will saturate Relation between and I field is no longer linear IfIf Magnetization curve

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Since for constant speed Ea the curve can be represented by E a vs I f EaEa I field Magnetization curve 11 Reduced speed 22 33 1 > 2 > 3

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