Back E.M.F of DC Motor and Equation


What is Back E.M.F. in DC Motor :


     When the armature of a d.c. motor rotates, the windings or conductors on the armature also rotate in the magnetic field. According to " Faraday's Laws of Electro-Magnetic Induction " e.m.f. is induced in the conductors, whose direction, as found by " Fleming's Right-Hand Rule ", is in opposition to the applied voltage. The emf induced in the armature winding is in the opposite direction, hence it is referred to as back e.m.f. Eb of the motor. This back emf tries to oppose applied voltage V, but it has to drive armature current Ia against the opposing of back emf Eb.

Back E.M.F of DC Motor and Equation


Where  Ra  =  armature resistance

Induced e.m.f or Back e.m.f.,


     Back e.m.f. depends upon armature speed. If speed is high Eb is high and hence Iis small. If speed is less, the Eb is less, hence more current flows to develop torque.



Formula for Back e.m.f of different DC Motors :


We know the induced e.m.f in a dc generator is found as


     In d.c. motor also the e.m.f is induced in the same way but it is opposite to the supply voltage hence, it is known as back or counter e.m.f and is given by the same formula as



Equivalent Circuit of DC Motor and Back EMF's :


i. Separately excited DC Motor :

     The field winding of these motors is energized from an external dc source.

Back E.M.F of DC Motor and Equation
V  =  E+  Ia R + BCD

Where
  • BCD = brush contact drop ( usually 1V / brush )
  • R=   armature ( winding ) resistance


ii. DC Shunt Motor :

     In a dc shunt motor field, winding is connected in parallel with the armature.

Back E.M.F of DC Motor and Equation
IL  =   Ia  + Ish
Ish  =  V / Rsh
V  =  Eb  +  Ia R +  BCD

iii. DC Series Motor :

     The field winding of these motors is connected in series with the armature and carries the same current.

Back E.M.F of DC Motor and Equation
IL   Ise Rse  =   I
V   =   Eb  Ise  Rse  +  Ia Ra   +  BCD
=  Eb  +  I( Rse + R)  +  BCD


iv. Short Shunt Compound Motor :

     It is a combination of shunt and series. But, shunt winding is connected across armature only. Hence short shunt motor.

Back E.M.F of DC Motor and Equation



V. Long Shunt Compound Motor :

     The shunt winding is connected across the combination of armature and series fields. Hence know as a long-shunt compound motor.

Back E.M.F of DC Motor and Equation
Ise  =   Ia
IL   Ise + Ish  =  Ia + Ish
Ish  =  V / Rsh
V  =  Eb  +  Ise  Rse  +  Ia  Ra  +  BCD

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