In case the back e.m.f. and the speed of a D.C. motor are doubled, the torque developed by the motor will

The correct answer is: C. Increase four folds

The torque developed by a DC motor is given by the following equation:

$$T = K \frac{V_a – Eb}{R}$$

where:

• $T$ is the torque developed by the motor
• $K$ is the torque constant of the motor
• $V_a$ is the applied voltage to the motor
• $Eb$ is the back EMF of the motor
• $R$ is the armature resistance of the motor

If the back EMF and the speed of the motor are doubled, then the torque developed by the motor will increase four folds. This is because the back EMF is proportional to the speed of the motor, and the torque constant is a constant. Therefore, the torque developed by the motor is proportional to the applied voltage to the motor divided by the back EMF of the motor. When the back EMF and the speed of the motor are doubled, the torque developed by the motor will increase four folds.

Here is a brief explanation of each option:

• Option A: The torque developed by the motor will remain unchanged. This is not correct because the back EMF and the speed of the motor are doubled. When the back EMF and the speed of the motor are doubled, the torque developed by the motor will increase four folds.
• Option B: The torque developed by the motor will reduce to one-fourth value. This is not correct because the back EMF and the speed of the motor are doubled. When the back EMF and the speed of the motor are doubled, the torque developed by the motor will increase four folds.
• Option C: The torque developed by the motor will increase four folds. This is correct because the back EMF and the speed of the motor are doubled. When the back EMF and the speed of the motor are doubled, the torque developed by the motor will increase four folds.
• Option D: The torque developed by the motor will be doubled. This is not correct because the back EMF and the speed of the motor are doubled. When the back EMF and the speed of the motor are doubled, the torque developed by the motor will increase four folds.