The torque developed by a d.c motor is directly proportional to

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Option A: Flux per pole $	imes$ Armature current

Explanation & Concepts:
The torque developed by a DC motor, known as electromagnetic torque ($T_e$ or $T_a$), is directly proportional to the magnetic flux per pole ($Phi$) and the armature current ($I_a$). This relationship is derived from the Lorentz force law applied to current-carrying conductors within a magnetic field.

Working Principle: In a DC motor, the armature winding carries current $I_a$ in the presence of a magnetic field produced by the field poles ($Phi$). According to the principle of electromagnetic force, every conductor in the magnetic field experiences a force $F = BIl$. Since the torque is the product of this force and the radius of the armature, the torque becomes proportional to the product of flux density (dependent on $Phi$) and the armature current $I_a$.

Key Formulas: $T_a = K_a \Phi I_a$ — where $K_a = \frac{PZ}{2\pi A}$ is the machine constant; $T_a \propto \Phi I_a$ — the proportionality relationship

Key Points: The constant $K_a$ depends on the number of poles (P), total conductors (Z), and parallel paths (A).; In a shunt motor, flux is nearly constant, making torque primarily dependent on armature current.; In a series motor, flux is dependent on $I_a$ (before saturation), leading to $T_a \propto I_a^2$.

Advantages: High starting torque in DC series motors.; Linear relationship allows for precise speed and torque control.

Disadvantages: Torque pulsation due to commutation.; Mechanical limitations of the commutator at high speeds.

Applications: Electric traction systems.; Industrial hoists and cranes.; Variable speed drive applications.

Additional Info: Option B and C are incorrect because torque is not a function of armature resistance ($R_a$), which instead affects power loss and speed regulation.. The equation $T_a = K_a \Phi I_a$ is fundamental for analyzing the mechanical characteristic curves of all DC machines.

Answer: A is correct — The electromagnetic torque developed by a DC motor is given by the product of flux per pole and the armature current ($T_a \propto \Phi I_a$).

Exam Tip: Always remember that in DC motors, torque is determined by the interaction between the field flux and armature current, whereas speed is determined by the back EMF and flux.

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Option B: Armature resistance $	imes$ Applied voltage

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Option C: Armature Resistance $	imes$ Armature current

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Option D: Square of armature resistance

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