The electrical characteristic is presented by plotting torque against armature current. Torque is directly proportional to armature current. In direct current series motors, the armature is connected in series with field winding. As such, the square of the armature current increases as the torque increases with the exception of magnetic saturation. Torque is also directly proportional to flux.
Without some mechanical load, never start a series motor. This is because speed is inversely proportional to armature current. A simple demonstration shows that when armature current is very small, speed becomes increasingly dangerous. In the case of heavy loads, the armature current becomes large hence lowering the speed. However, in the case of a load current change, this characteristic may be negligible. However, it does not change the fact that flux is directly proportional to armature current.
The mechanical characteristic is shown by speed being inversely proportional to torque. As such, when the speed is high, torque becomes low. Generally, one may note that when a load is added on the DC series motor, it decreases back Emf armature current, which results in an increased net voltage that consequently leads to increased current in the series field. If the current in the field coil is so high that it saturates the magnetic core, the magnetic flux increases slowly as compared to the current beyond saturation.