# Back E.M.F of DC Motor and Equation

## What is Back EMF in DC Motor :

When the armature of a dc motor rotates, the windings or conductors on the armature also rotate in the magnetic field. According to "Faraday's Laws of Electro-Magnetic Induction" emf 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 emf 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.

Where Ra = armature resistance and expression for induced emf or Back emf is given as,

Back emf depends upon armature speed. If speed is high Eb is high and hence Ia is small. If speed is less, the Eb is less, hence more current flows to develop torque.

## Formula for Back EMF of different DC Motors :

#### We know the induced emf in a dc generator is found as,

In dc motor also the emf is induced in the same way but it is opposite to the supply voltage hence, it is known as back or counter emf and is given by the same formula as,

## Equivalent Circuit of DC Motor and Back EMF's :

### Separately excited DC Motor :

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

V = Eb + IaRa + BCD

### DC Shunt Motor :

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

IL = Ia + Ish
Ish = V/Rsh
V = Eb + IaRa + BCD

### DC Series Motor :

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

IL = IseRse = Ia
V = Eb + IseRse + IaRa + BCD
V = Eb + Ia (Rse + Ra) + BCD

### Short Shunt Compound Motor :

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

### 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.

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