The speed of a DC motor can be varied by varying

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Option D: any of the above

Explanation & Concepts:
The speed of a DC motor is governed by its fundamental back EMF equation, which relates speed to terminal voltage, armature resistance, and magnetic flux. By manipulating any of these variables, the motor speed can be effectively controlled to suit different operational requirements.

Working Principle: According to the speed equation $N = K \frac{V - I_a R_a}{\Phi}$, the speed $N$ is directly proportional to the back EMF ($V - I_a R_a$) and inversely proportional to the flux per pole $\Phi$. Therefore, changing the applied voltage ($V$), inserting series resistance in the armature circuit ($R_a$), or varying the field current ($I_f$) which affects $\Phi$, provides distinct methods of speed control.

Key Formulas: $N = K \frac{V - I_a R_a}{\Phi}$ — Fundamental speed equation of a DC motor; $E_b = \frac{P \Phi Z N}{60 A}$ — Expression for back EMF

Key Points: Flux control method (Field current variation) provides speeds above the rated speed.; Armature resistance control provides speeds below the rated speed.; Voltage control (Ward-Leonard system) allows wide range speed control.; The armature resistance control method is inefficient due to high $I^2R$ power losses.

Advantages: Field control is highly efficient as it involves small field currents.; Armature control is simple and inexpensive for small motors.; Ward-Leonard system offers smooth and precise wide-range speed control.

Disadvantages: Armature resistance control results in poor speed regulation at low speeds.; Field weakening can lead to instability if the flux is reduced too much.; Ward-Leonard system requires an additional motor-generator set, increasing cost and footprint.

Applications: Steel rolling mills; Electric locomotives; Conveyor systems; Printing presses

Additional Info: The speed-torque characteristic changes significantly based on the method used.. In shunt motors, field current variation is the most common method for higher speeds.

Answer: D is correct — The DC motor speed can be controlled by any of these methods as they all affect the back EMF or the magnetic flux, which are the primary determinants of speed.

Exam Tip: Always remember: Armature control varies speed below base speed, while field control varies speed above base speed.

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Option A: field current

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Option B: applied voltage

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Option C: resistance in series with armature

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