Counter EMF of the DC motor is

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Option A: Less than the applied voltage

Explanation & Concepts:
The counter EMF (or back EMF), denoted as $E_b$, is the induced voltage generated by a DC motor acting as a generator while it rotates in a magnetic field. According to Lenz's law, this voltage always opposes the applied terminal voltage $V$, and due to the inherent voltage drop across the internal armature resistance ($I_a R_a$), it must always be less than the applied voltage to allow current to flow.

Working Principle: When a DC motor is connected to a supply voltage $V$, current $I_a$ flows into the armature. As the armature conductors cut the magnetic field, an EMF is induced ($E_b = \frac{P \Phi Z N}{60 A}$). The relationship between the supply voltage and back EMF is governed by Kirchhoff's Voltage Law: $V = E_b + I_a R_a$. Since $I_a R_a > 0$ under normal operating conditions, $E_b$ must be strictly less than $V$.

Key Formulas: $E_b = V - I_a R_a$ — The fundamental voltage balance equation for a DC motor armature.; $E_b = \frac{P \Phi Z N}{60 A}$ — The EMF equation representing the back EMF generation principle.

Key Points: Back EMF is proportional to speed and flux ($E_b \propto \Phi N$).; At standstill (starting), $N = 0$, so $E_b = 0$, leading to high starting current unless controlled.; If $E_b = V$, the motor would draw zero current and perform no work.; If $E_b > V$, the device acts as a generator, not a motor.

Advantages: Provides self-regulation of armature current based on mechanical load.; Limits the current drawn from the supply to a safe level during operation.

Disadvantages: High starting current is possible due to $E_b = 0$ at start.; Requires external starting resistors or starters to prevent winding damage.

Applications: Industrial variable speed drives.; Electric traction systems.; Battery-operated small motor devices.

Additional Info: The back EMF is often termed 'Counter EMF' because it opposes the applied voltage source.. Option B is incorrect because if $E_b > V$, the machine enters regenerative braking mode (generating).. Option C is incorrect because it would result in zero current, preventing the production of electromagnetic torque.

Answer: A is correct — The counter EMF $E_b$ is always less than the applied terminal voltage $V$ because a portion of the voltage is consumed by the armature ohmic drop ($I_a R_a$).

Exam Tip: Remember: $E_b$ is directly proportional to speed $N$. At no-load, $N$ reaches its maximum, causing $E_b$ to be nearly equal to $V$, resulting in very low armature current.

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Option B: More than the applied voltage

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Option C: Equal to the applied voltage

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Option D: None of the above

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