Explain the concept of back emf in a DC motor.

When the armature of a DC motor rotates in the magnetic field, its conductors cut the flux, so an EMF is induced in them (generator action, Faraday's law). By Lenz's law this induced EMF opposes the applied voltage V; hence it is called back EMF (counter EMF) E_b.

\[ E_b = \frac{\phi ZNP}{60A}\ \text{V},\qquad V = E_b + I_aR_a \Rightarrow I_a = \frac{V - E_b}{R_a} \]

Significance:

• It makes the motor self-regulating: at light load speed rises, E_b increases and I_a falls; when load increases, speed drops slightly, E_b falls and the motor draws more current to develop more torque.
• At starting N = 0, so E_b = 0 and I_a = V/R_a is very large; hence a starter (series resistance) is needed.
• E_bI_a is the electrical power converted into mechanical power (gross mechanical power developed).