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“ Series motors are never used unless they are directly connected to load”- why?

In a series motor the flux depends upon the current in the series field, which is the same current that flows through the armature. At light loads the armature current is small; therefore the flux and torque are small. An increase in the load increases both the armature current and the flux. The basic speed equation                                    S =        Vt   - IaRa   - IaRa           KФ Since the current in the series field is the armature current, the equation may be rewritten substituting Ia for Ф.                                        S =    Vt   - IaRa   - IaRa           KIa With no load connection to the motor the value of I is very small. The numerator of the speed equation is large, while the denominator is very small, indicating that the speed of   the motor   will be extremely large. In fact, the speed of the motor may reach such a value as to cause the centrifugal force to destroy the motor. It is

The speed versus armature current and torque versus armature current characteristics of dc motor

Torque versus armature   current characteristics of DC motor : The torque developed   by the motor would therefore be directly dependent upon the armature current as indicated by the torque equation ,T=K ΦIa. Increasing the armature current would increase the torque and vice versa.   Shunt motor : For the shunt motor shunt field is connected accross the line, the flux in the machine will remain essentially constant . So, for shunt motor, T=KΦfIa Compound   Motor: The current in the armature must also pass through the series field winding. The series winding may be connected comulatively were the flux due the series field will aid the shunt field flux. In cumulative compound motor the series field flux is additive with the field flux. But in the differentially compound motor the series field flux is substractive with main field flux. Total flux does not remain constant in compound motor as it does in the shunt motor. Cumulative compound motor T=k(Φf+Φs)Ia