BACK E.M.F:

When the motor armature is rotate, hence the conductor s also rotate and cut fluxes. According the law of electromagnetic induction an e.m.f is produced, is in opposition of the supply voltage. Because of its opposite direction it is referred to as counter e.m.f  or Back  e.m.f. [ EB]
b = ΦZN * [P / A] volt Where N is r.p.s
Back e.m.f depends on armature speed. If speed is high Eb is high. If speed is low Eb is low.
VOLTAGE EQUATION OF A MOTOR:

The voltage V applied across the motor armature has to

1.      Overcame the back e.m.f Eb

2.      Supply the armature ohomic  drop IaRa

[ V = Eb + IaRa ] Voltage equation of a motor.

Now, mollifying both side by Ia

[ Via = EbIa + Ia2Ra ]

Via     = Electrical input to the armature.

EbIa   = Mechanical power developed in the armature.

Ia2Ra = Cu loss in the armature.

Out of the armature input, some is wasted in I2R loss and the rest is converted into mechanical power within the armature.

Motor efficiency is given by the ratio of power developed by the armature to its input

[ EbIa / VIa ] = [ Eb / V ]

High the value of Eb as compared to V, higher the motor efficiency.
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