When a dc machine is loaded either as a motor or as a generator, the rotor conductor carry current.These conductor lie in the magnetic field of air gap. thus each conductor experiences a force. the conductor lie near the surface of the rotor at a common radius from its centre. Hence a torque is produced around the circumference of the rotor and the rotor starting rotating.

When the machine operates as a generator at constant speed, this torque is equal and opposite to that provided by the prime-mover. when the machine is operating as a motor the torque is transferred to the shaft of the rotor and drives the mechanical load.

The expression for torque is the same for generator or motor. It can be derive as

The voltage equation of d.c. motor

V = E + I

Multiplying both sides of equation by I

VI

But

VI

I

We also known that input = output + losses

EI

𝜏

The voltage equation of d.c. motor

V = E + I

_{a}R_{a }Multiplying both sides of equation by I

_{a }we, obtainVI

_{a}= EI_{a}+ I_{a}^{2}R_{a }But

VI

_{a}= Electrical power input to the armatureI

_{a}^{2}R_{a}= Copper loss in the armatureWe also known that input = output + losses

EI

_{a}=Electrical equivalent of gross mechanical power developed by the armature ( electromechanical power )𝜏

_{av}= Average electromechanical torque developed by the armature in newton meters (Nm)
At this value of torque the electromechanical power conversion takes place.

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