If the load current and flux of a DC motor are held constant, and voltage applied across its armature is increased by 10%, its speed will: 

Explanation:

Effect of Armature Voltage on the Speed of a DC Motor

Definition: In a DC motor, the speed is primarily determined by the applied voltage across the armature, the flux produced by the field winding, and the load torque. The relationship between these parameters can be derived from the fundamental equation of a DC motor:

Speed Equation:

The speed (N) of a DC motor is given by:

N = (V - IaRa) / (kΦ)

Where:

• N = Speed of the motor (in rpm)
• V = Voltage applied across the armature
• Ia = Armature current
• Ra = Armature resistance
• Φ = Flux per pole produced by the field winding
• k = Motor constant (depends on the motor's construction)

In the given problem, the load current (Ia) and flux (Φ) are held constant, and the voltage applied across the armature (V) is increased by 10%. Let us analyze how this affects the speed of the motor.

Working Principle:

When the armature voltage (V) is increased, the numerator of the speed equation increases while the denominator remains constant (since both flux Φ and load current Ia are unchanged). Therefore, the speed of the motor increases. Specifically, a 10% increase in V results in a proportional increase in the speed of the motor.

Mathematically:

New Speed (N') = (1.1 × V - IaRa) / (kΦ)

Since the load current and flux are constant, the change in speed is directly proportional to the change in voltage. Thus, when the armature voltage is increased by 10%, the speed of the DC motor also increases by 10%.

Correct Option: Option 3: Increase by 10%

Key Insight: The speed of a DC motor is directly proportional to the applied armature voltage when other factors such as flux and load current are constant. This relationship is a fundamental characteristic of DC motors.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Decrease by 10%

This option is incorrect. Increasing the armature voltage while keeping the flux and load current constant leads to an increase in speed, not a decrease. A decrease in speed would require a reduction in the applied voltage or an increase in the load torque, neither of which is mentioned in the problem.

Option 2: Remain unchanged

This option is also incorrect. The speed of a DC motor cannot remain unchanged if the applied voltage across the armature is varied. The speed is directly proportional to the armature voltage, so any change in voltage will result in a corresponding change in speed.

Option 4: Increase by 20%

This option is incorrect because the speed increase is directly proportional to the change in armature voltage. A 10% increase in voltage results in a 10% increase in speed, not 20%. A 20% increase in speed would require a 20% increase in the applied voltage.

Option 5: (Not Provided)

Since this option is not explicitly stated, it can be disregarded for the analysis.

Conclusion:

Understanding the relationship between the applied voltage, flux, and speed of a DC motor is crucial for analyzing its behavior under varying conditions. In this problem, increasing the armature voltage by 10% while keeping the load current and flux constant results in a 10% increase in the speed of the motor. This proportional relationship is a fundamental characteristic of DC motors and is derived from the speed equation.