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What is meant by back e.m.f?

Back e.m.f.: When the motor armature rotates,the conductors also rotate and hence cut the flux.In accordance with the laws of electromagnetic induction, e.m.f.is induced in them whose direction,as found by Fleming , s Right-hand Rule,is in opposition to the applied voltage. Because of its opposite direction, it is referred to as counter e.m.f. or back e.m.f.E b.                                                                                                                                                                                Fig:1 Prove that the gross power developed by a DC motor is maximum when the back e.m.f. (E b ) equals to the half of the applied voltage(V):  Back e.m.f.E b =V t -I a R a   Where V t =applied terminal voltage,     I a =armature current,      R a =armature resistance                                                                                                                                                            T