Back emf in dc motor

Back emf. When the armature of a DC motor rotates, its conductors cut the main flux, and by Faraday's law an emf is induced in them. By Lenz's law this emf opposes the applied voltage (the cause producing it), so it is called the back (counter) emf:

$$E_b=\frac{P\phi ZN}{60A}$$

and the armature current is

$$I_a=\frac{V-E_b}{R_a}$$

Significance:

1. Acts as a governor. If load increases, speed falls, $E_b$ falls, $I_a$ rises, and torque increases to meet the load. If the load falls, the opposite occurs. The motor thus adjusts the input current automatically.
2. Limits the armature current. At standstill $E_b=0$, so the starting current $V/R_a$ is very large (a starter is therefore needed). At running speed, $E_b$ is close to $V$ and current is small.
3. Indicates energy conversion. The electrical power converted to mechanical power is $E_bI_a$; without back emf there would be no conversion.
4. Determines speed: $N\propto\frac{E_b}{\phi}$.