Voltage equation of a D.C. Motor
In case of a generator, generated emf has to supply armature resistance drop and remaining part is available across the load as a terminal voltage. But in case of d.c. motor, supply voltage V has to overcome back emf Eb which is opposing V and also various drops as armature resistance drop IaRa, brush drop etc.
Hence the voltage equation of a d.c. motor can be written as,
Neglecting the brush drop, the generalized voltage equation is,
In case of Motor
In case of Generator
In case of motor, the back emf is always less than the supply voltage. But is very small hence under normal running conditions, the difference between back emf and the supply voltage is very small. The net voltage across the armature is the difference between the supply voltage and back emf which decides the armature current. Hence from the voltage equation we can write,
Power Equation of a D.C. Motor
The voltage equation of a d.c. motor is given by,
Multiplying both sides of the above equation by we get,
This equation is called power equation of a d.c. motor.
= Net electrical power input to the armature measured in watts.
= Power loss due to the resistance of the armature called armature copper loss.
So difference between and i.e. input – losses gives the output power.
So is called electrical equivalent of gross mechanical power developed by the armature. This is denoted as
Gross mechanical power developed in the armature = Power input to the armature – Armature copper loss
Condition for Maximum power
For a motor from power equation it is known that
For maximum gross mechanical power