# Characteristics of DC Series Motor

1. Electrical Characteristics :

In a d.c. series motor, the armature current and series field current are same and therefore Φ Ia. The armature torque is equal to

Ta Φ Ia or
Ta Ia2

This is true till the point of magnetic saturation. When Ia is zero, torque is also zero and when I is small torque is also small. Since is proportional to square of the armature current the curve is parabolic. After saturation Φ is almost constant and for any increase in armature current torque increases linearly i.e., Ta Ia. The shaft torque is less than armature torque by rotational losses, The curve is shown in Fig.

2. Speed and Armature Current Characteristics :

For a d.c. series motor

Eb = V - Ia (Ra +Rse) and Eb = ΦN x ZP/60A
or Eb = KaΦN
Where Ka = ZP/60A

Substituting the values,

KaΦN = V - Ia (Ra +Rse)
or N = V - Ia (Ra +Rse)/ KaΦ
or N = V/ KaΦ - Ia (Ra +Rse)/ KaΦ

But for a dc series motor, Φ Ia, therefore

N = V/ KbIa(Ra +Rse)/ Kb ; where Kb = Ia/Ka

From the above equation, it is seen that neglecting armature reaction and with saturation the speed-current characteristics of d.c. series motor is hyperbolic as shown in Fig. When la increases Φ also increase but due to demagnetisation effect of armature reaction and saturation, the air gap flux tends to remain constant and for constant flux Φ the term V/KaΦ remains constant and the term la [Ra + Rse]/ KaΦ increases with armature current linearly.
Thus for larger values of armature current, the curve takes a straight line path. At no load the armature current is small and so the armature drop Ia (Ra + Rse) and can be considered negligible as compared to terminal voltage.

Then N = V/KaΦ, But Φ Ia,therefore N = V/Kbla

On no load when the armature current tends to zero, the speed tends to infinity. Therefore, the no load speed of d.c. series motor is dangerously high and due to this reason the d.c. series motor must not be started without a load. The curve is shown in Fig.

3. Speed-Torque Characteristics :

The torque of d.c. series motor is proportional to the square of armature current i.e.

Ia2 Ta or
Ia √Ta

Neglecting the armature reaction and saturation

N = V/KbIa  or  N = V/Kb√Ta

Squaring both sides

N2 =  V2/KcTa
or Ta  = V2/N2Kc
or Ta ∝ 1/N2

The speed torque characteristics is also hyperbolic in nature. But with saturation and armature reaction large torque requires larger currents and these large currents tends to make the air gap flux constant and the effect is Ta Ia instead of Ta Ia2. The curves approaches straight line as shown in Fig.