SOLUTION

Series Connection:

In DC machine, T = kφi

where

k = number of poles and the number of turns in the winding.
Φ = flux per pole
i =  current.

If saturation of core is neglected, then Flux is proportional to field current.

So Torque= k *field current*armature current.

For DC series machine, Armature current = Field Current,
Therefore, Torque = k × I_a²

If we apply AC then both, during positive as well as negative half cycle, torque is positive from above relation. So, torque is unidirectional, but due to AC, it will be pulsating.

Parallel connection:

• But, In the case of parallel connection, it won’t rotate at all and will start humming and will create vibrations, as a torque produced by positive and negative cycle will cancel out each other. D.C. motor will be heated up.