Why a dc series motor has a high starting torque?

1. **Field and Armature Current Relationship**: At startup, the armature current is high because the motor initially has low resistance and no back EMF (electromotive force). Since the field windings are in series with the armature, the high armature current also flows through the field windings, creating a strong magnetic field.

2. **Increased Magnetic Flux**: The strong magnetic field generated by the high current in the field windings results in a large amount of magnetic flux. According to the motor’s torque equation \( T = k \cdot \Phi \cdot I_a \) (where \( \Phi \) is the magnetic flux, and \( I_a \) is the armature current), the torque is proportional to both the flux and the armature current. With both being high at startup, the torque is also high.

3. **Torque Characteristics**: The torque of a series motor is proportional to the square of the armature current. At startup, since the armature current is high, the torque produced is correspondingly high, making the motor capable of handling heavy loads at startup.

This characteristic makes DC series motors particularly useful in applications where high starting torque is essential, such as in traction systems and certain types of machinery.