**T**and

_{a}∝ ɸ.I_{a}**N ∝ E**

_{b}/ɸThese above equations can be studied at - emf and torque equation of dc machine. For a DC motor, magnitude of the back emf is given by the same emf equation of a dc generator i.e. E

_{b}= PɸNZ / 60A. For a machine, P, Z and A are constant, therefore, N ∝ E

_{b}/ɸ

### Characteristics of DC series motors

####
Torque vs. armature current (T_{a}-I_{a})

This characteristic is also known as **electrical characteristic**. We know that torque is directly proportional to the product of armature current and field flux, T

_{a}∝ ɸ.I

_{a}. In DC series motors, field winding is connected in series with the armature, i.e. I

_{a}= I

_{f}. Therefore, before magnetic saturation of the field, flux ɸ is directly proportional to Ia. Hence, before magnetic saturation Ta α Ia

^{2}. Therefore, the Ta-Ia curve is parabola for smaller values of Ia.

After magnetic saturation of the field poles, flux ɸ is independent of armature current Ia. Therefore, the torque varies proportionally to Ia only, T ∝ Ia.Therefore, after magnetic saturation, Ta-Ia curve becomes a straight line.

The shaft torque (Tsh) is less than armature torque (Ta) due to stray losses. Hence, the curve Tsh vs Ia lies slightly lower.

The shaft torque (Tsh) is less than armature torque (Ta) due to stray losses. Hence, the curve Tsh vs Ia lies slightly lower.

In DC series motors, (prior to magnetic saturation) torque increases as the square of armature current, these motors are used where high starting torque is required.

#### Speed vs. armature current (N-Ia)

We know the relation, N ∝ E_{b}/ɸ

For small load current (and hence for small armature current) change in back emf Eb is small and it may be neglected. Hence, for small currents speed is inversely proportional to ɸ. As we know, flux is directly proportional to Ia, speed is inversely proportional to Ia. Therefore, when armature current is very small the speed becomes dangerously high. That is

But, at heavy loads, armature current Ia is large. And hence, speed is low which results in decreased back emf Eb. Due to decreased Eb, more armature current is allowed.**why a series motor should never be started without some mechanical load**.#### Speed vs. torque (N-Ta)

This characteristic is also called as**mechanical characteristic**. From the above two

**characteristics of DC series motor**, it can be found that when speed is high, torque is low and vice versa.

### Characteristics of DC shunt motors

#### Torque vs. armature current (Ta-Ia)

In case of DC shunt motors, we can assume the field flux ɸ to be constant. Though at heavy loads, ɸ decreases in a small amount due to increased armature reaction. As we are neglecting the change in the flux ɸ, we can say that torque is proportional to armature current. Hence, the Ta-Ia characteristic for a dc shunt motor will be a straight line through the origin.Since heavy starting load needs heavy starting current,

**shunt motor should never be started on a heavy load**.

#### Speed vs. armature current (N-Ia)

As flux ɸ is assumed to be constant, we can say N ∝ Eb. But, as back emf is also almost constant, the speed should remain constant. But practically, ɸ as well as Eb decreases with increase in load. Back emf Eb decreases slightly more than ɸ, therefore, the speed decreases slightly. Generally, the speed decreases only by 5 to 15% of full load speed. Therefore,**a shunt motor can be assumed as a constant speed motor**. In speed vs. armature current characteristic in the following figure, the straight horizontal line represents the ideal characteristic and the actual characteristic is shown by the dotted line.

### Characteristics of DC compound motor

DC compound motors have both series as well as shunt winding. In a compound motor, if series and shunt windings are connected such that series flux is in direction as that of the shunt flux then the motor is said to be cumulatively compounded. And if the series flux is opposite to the direction of the shunt flux, then the motor is said to be differentially compounded. Characteristics of both these compound motors are explained below.**(a) Cumulative compound motor**

Cumulative compound motors are used where series characteristics are required but the load is likely to be removed completely. Series winding takes care of the heavy load, whereas the shunt winding prevents the motor from running at dangerously high speed when the load is suddenly removed. These motors have generally employed a flywheel, where sudden and temporary loads are applied like in rolling mills.

**(b) Differential compound motor**

Since in differential field motors, series flux opposes shunt flux, the total flux decreases with increase in load. Due to this, the speed remains almost constant or even it may increase slightly with increase in load (N ∝ E

_{b}/ɸ). Differential compound motors are not commonly used, but they find limited applications in experimental and research work.