--- title: "Unidirectional torque in dc machine" subject: "Electrical Machines" chapter: 4 key: "semester_4/electrical_machines:unidirectional-torque-dc-machine" source: https://www.bctengineer.com/q/semester_4/electrical_machines/unidirectional-torque-dc-machine site: BCT Engineering --- # Unidirectional torque in dc machine Electrical Machines · Chapter 4: DC Motor - Asked in: 2079 Jestha, 8 marks - Video: [Torque Equation of a DC motor | BEE In Hindi](https://www.youtube.com/watch?v=_Jy4wchNZh0) — Last moment tuitions - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/unidirectional-torque-dc-machine - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-4 ## Question How unidirectional torque is produced in dc machine when armature is supplied by dc source and field winding is supplied by dc current? What are the factors affecting torque produced? ## Short answer Due to the commutator, armature conductors under N and S poles carry currents in opposite directions, so force direction is same, producing unidirectional torque. Torque T = (ZP/2πA) Φ Ia depends on flux per pole, armature current, number of conductors, poles, and parallel paths; for a given machine T ∝ Φ Ia. ## Answer #### Production of unidirectional torque When both the armature (through the brushes) and the field winding are supplied with direct current, the armature conductors carry current in a magnetic field, so each conductor experiences a force $F = BIl$ (Fleming's left-hand rule). - Conductors under the **N pole** carry current in one direction (into the page); those under the **S pole** carry it in the opposite direction (out of the page). - Because the field direction under the two poles is also opposite, the forces on the two sets of conductors act in the **same rotational sense**, so a net torque turns the armature. When the armature turns, a conductor moves from under the N pole to under the S pole. If its current stayed the same, the force on it would reverse. The **commutator** prevents this: its segments reverse the connection of the conductor to the brushes at the moment it crosses the neutral axis, so the current in the conductor reverses at the same time as the field. The product $B\times I$ keeps the same sign, so the torque stays in the **same direction** (unidirectional). ```text Under N pole Under S pole current (x) ---> current (.) after commutation force -> up force -> up (same sense of rotation) ``` #### Factors affecting the torque From $T = \dfrac{ZP}{2\pi A}\Phi I_a$, the torque depends on: 1. **Flux per pole** $\Phi$ (field current and magnetic circuit). 2. **Armature current** $I_a$ (load and supply voltage). 3. **Number of armature conductors** $Z$. 4. **Number of poles** $P$. 5. **Number of parallel paths** $A$ (type of winding: lap $A = P$, wave $A = 2$). For a given machine $Z$, $P$, $A$ are fixed, so $T\propto\Phi I_a$. For a shunt motor $T\propto I_a$; for an unsaturated series motor $T\propto I_a^2$. Armature reaction (which weakens the flux) and the brush position also change the torque. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does the armature of a DC machine experience a force when both armature and field are supplied with DC? A. Armature conductors carry current in a magnetic field, giving F = BIl B. The commutator itself produces the force C. The brushes attract the armature D. Eddy currents in the core produce the force Answer: A. Current-carrying conductors in the field flux each feel a force F = BIl (Fleming's left-hand rule). (Key point: Force on conductors) 2. Conductors under N and S poles carry opposite currents. Why is the net torque still in one direction? A. Because the forces cancel and the inertia keeps it turning B. Because the field direction is also opposite under the two poles, so the forces act in the same rotational sense C. Because only the N-pole conductors carry current D. Because the brushes are at the poles Answer: B. Both current and field reverse between the poles, so B x I keeps its sign and the forces add up to a net torque. (Key point: Same rotational sense) 3. What does the commutator do to keep the torque unidirectional? A. It reverses the field flux as the conductor moves B. It increases the armature current C. It reverses the conductor current as it crosses the neutral axis, in step with the field reversal D. It removes armature reaction Answer: C. Without commutation, a conductor moving from N to S pole would see its force reverse; the commutator reverses its current at that moment. (Key point: Role of commutator) 4. For a given machine, which quantities decide the torque in T = (ZP/2piA) Phi Ia? A. Z, P and A alone B. Speed and back emf only C. Flux per pole and armature current D. Brush width and commutator size Answer: C. Z, P, A are fixed for a machine, so T is proportional to flux per pole and armature current. 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