If Ta be the armature torque and Ia be the armature current then which of the following relation is

Question

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?

Examoogle · Accepted Answer

$T_a \propto I_a^2$

Explanation: 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.

Working Principle: The torque produced by a DC motor is given by $T_a \propto \Phi I_a$. In a DC series motor, the field winding is in series with the armature, so the field flux $\Phi$ is directly proportional to $I_a$ ($\Phi \propto I_a$). Substituting this into the torque equation yields $T_a \propto I_a \cdot I_a = I_a^2$. This quadratic relationship holds true only in the linear region of the magnetization curve before the magnetic core reaches saturation.

Key Formulas: $T_a \propto \Phi I_a$ — General torque equation for DC motor; $\Phi \propto I_a$ — Flux relation in DC series motor before saturation; $T_a = k_a \Phi I_a$ — Exact electromagnetic torque equation

Key Points: The armature and field currents are identical ($I_a = I_f$).; Linear region refers to the unsaturated state of the magnetic core.; After saturation, the flux becomes nearly constant, making $T_a \propto I_a$.

Advantages: High starting torque due to quadratic relationship.; Well-suited for traction and heavy-duty starting applications.

Disadvantages: Unstable at no-load (dangerous speed runaway).; Cannot be operated without a mechanical load coupled to the shaft.

Applications: Electric locomotives and trains.; Cranes, hoists, and industrial winches.

Additional Info: 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.

Answer: B is correct — Before saturation, the flux $\Phi$ is directly proportional to $I_a$, resulting in $T_a \propto I_a^2$.

Exam Tip: 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.

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