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Examoogle • User • info@examoogle.com • EE-2024-8821
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If Ta be the armature torque and Ia be the armature current then which of the following relation is valid for DC series motor before saturation?
Ta∝Ia
Ta∝Ia2
Ta∝Ia1
Ta∝Ia21
Ta∝Ia2
Quick Summary: In a DC series motor, the armature current $I_a$ flows through the field winding because the field and armature are connected in series. Since the flux $\Phi$ produced is directly proportional to the current $I_a$ (before magnetic saturation), the armature torque $T_a$ follows a square-law relationship with the current.
In a DC series motor, the armature current Ia flows through the field winding because the field and armature are connected in series. Since the flux Φ produced is directly proportional to the current Ia (before magnetic saturation), the armature torque Ta follows a square-law relationship with the current.
Ta∝ΦIa — General torque equation for DC motor
Φ∝Ia — Flux relation in DC series motor before saturation
Ta=kaΦIa — Exact electromagnetic torque equation
The torque produced by a DC motor is given by Ta∝ΦIa. In a DC series motor, the field winding is in series with the armature, so the field flux Φ is directly proportional to Ia (Φ∝Ia). Substituting this into the torque equation yields Ta∝Ia⋅Ia=Ia2. This quadratic relationship holds true only in the linear region of the magnetization curve before the magnetic core reaches saturation.
The armature and field currents are identical (Ia=If).
Linear region refers to the unsaturated state of the magnetic core.
After saturation, the flux becomes nearly constant, making Ta∝Ia.
High starting torque due to quadratic relationship.
Well-suited for traction and heavy-duty starting applications.
Unstable at no-load (dangerous speed runaway).
Cannot be operated without a mechanical load coupled to the shaft.
Electric locomotives and trains.
Cranes, hoists, and industrial winches.
Saturation occurs when the iron core can no longer increase flux density significantly with increased magnetizing current.
Option A is incorrect as it represents the shunt motor characteristic or saturated series motor.
Options C and D suggest an inverse relationship, which contradicts the fundamental torque principles of DC motors.
B is correct — Before saturation, the flux Φ is directly proportional to Ia, resulting in Ta∝Ia2.
Always remember that in DC motors, shunt machines have relatively constant flux resulting in linear torque characteristics, while series machines offer high initial torque due to the square law.