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 the " 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 I is small. If speed is less, the Eb is less, hence more current flows to develop torque.

Formula for Back e.m.f for 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 are energised from an external dc source.

Back E.M.F of DC Motor and Equation

V  =  E+  Ia R + BCD


     BCD = brush contact drop ( usually 1V / brush )

     R=   armature ( winding ) resistance    

R =  IL

(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 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 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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