### Characteristics of D.C. Series Motor

i) Torque - Armature current characteristics
In case of series motor the series field winding is carrying the entire armature current. So flux produced is proportional to the armature current.
...                   Φ  α  Ia
Hence      Ta  α Φ Ia  α Ia2
Thus torque in case of series motor is proportional to the square of the armature current. This relation is parabolic in nature as shown in the Fig. 1.

As load increases, armature current increases and torque produced increases proportional to the square of the armature current upto a certain limitt.
As the entire Ipasses through the series field, there is a property of an electromagnet called saturation, may occur. Saturation means though the current through the winding increases, the flux produced remains constant. Hence after saturation the characteristics take the place of straight line as flux becomes constant, as shown. The difference between Tand Tsh is loss torque Tf which is also shown in the Fig. 2.
At start as T  αIa2   , these types of motors can produce high torque for small amount of armature current hence the series motors are suitable for the applications which demand high starting torque.
ii) Speed - Armature current characteristics
From the speed equation we get,
N  α  (Eb/Φ)   αV - I Ra - I Rse)/ I                 as Φ α I   in case of series motor
Now the values of Ra and Rse are so small that the effect of change in  Ia on speed overrides the effect of change in V - I Ra - I Rse  on the speed.
Hence in the speed equation, Eb Vand can be assumed constant. So speed equation reduced to,
N α  1/Ia
So speed-armature current characteristics is rectangular hyperbola type as shown in the Fig. 2.
iii) Speed - Torque characteristics
In case of series motors,            T α Ia2      and   N α  1/Ia
Hence we can write,      N α  1/√T
Thus as torque increases when load increases, the speed decreases. On no load, torque is very less and hence speed increases to dangerously high value. Thus the nature of the speed-torque characteristics is similar to the nature of the speed-armature current characteristics.
The speed-torque characteristics of a series motor is shown in the Fig. 3.
 Fig. 3  N  Vs  T for series motor