The ratio of back EMF to voltage of a DC motor is an indication of: 

Explanation:

The ratio of back EMF to voltage of a DC motor is an indication of its efficiency.

To understand why efficiency is the correct answer, let's delve into the working of a DC motor and how back EMF and applied voltage affect its performance.

Working Principle of a DC Motor:

A DC motor operates on the principle that when a current-carrying conductor is placed in a magnetic field, it experiences a force. In a DC motor, the armature winding (the current-carrying conductor) is placed within the magnetic field created by the stator (field winding). When a DC voltage is applied to the armature winding, current flows through it, generating a magnetic field that interacts with the stator’s magnetic field, producing a torque that causes the armature to rotate.

Back EMF (Electromotive Force):

As the armature rotates, it cuts through the magnetic field lines, which induces a voltage in the armature winding known as back EMF (E_b). According to Lenz's Law, this induced voltage opposes the applied voltage (V) and is given by:

E_b = k * φ * ω

Where:

• k is a constant that depends on the construction of the motor.
• φ is the magnetic flux.
• ω is the angular velocity of the armature.

The back EMF increases with the speed of the motor. When the motor is running at a steady speed, the back EMF almost balances the applied voltage, and the current drawn by the motor is reduced to a level just sufficient to overcome friction, windage losses, and provide the necessary torque for the load.

Efficiency of a DC Motor:

Efficiency (η) of a DC motor is defined as the ratio of the mechanical power output to the electrical power input. It can be expressed as:

η = (P_out / P_in) * 100%

Where:

• P_out is the mechanical power output.
• P_in is the electrical power input.

The electrical power input (P_in) is given by:

P_in = V * I

Where:

• V is the applied voltage.
• I is the current drawn by the motor.

The mechanical power output (P_out) is given by:

P_out = (E_b * I) - (I² * R_a)

Where:

• E_b is the back EMF.
• I is the current drawn by the motor.
• R_a is the armature resistance.

From the above equations, we can see that the back EMF (E_b) plays a crucial role in determining the efficiency of the motor. When the motor is running at a higher efficiency, the back EMF will be closer to the applied voltage (V), meaning that most of the input electrical power is being converted into useful mechanical power, with minimal losses.

Therefore, the ratio of back EMF to the applied voltage is a direct indication of the efficiency of the motor. A higher ratio suggests higher efficiency, as more of the electrical input is being effectively converted into mechanical output with fewer losses.

Important Information

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

Option 1: Starting Torque

The starting torque of a DC motor is the torque it produces when it starts from a standstill. At the start, the back EMF is zero because the motor is not yet moving. Therefore, the starting torque is primarily determined by the applied voltage and the current flowing through the armature windings. The ratio of back EMF to voltage does not provide information about the starting torque.

Option 2: Speed Regulation

Speed regulation refers to the ability of the motor to maintain a constant speed under varying load conditions. While back EMF does play a role in speed regulation, the ratio of back EMF to voltage alone does not directly indicate speed regulation. Speed regulation depends on various factors, including the design of the motor and the control methods used.

Option 3: Running Torque

Running torque is the torque produced by the motor when it is running at a steady speed. While back EMF affects the current and hence the torque, the ratio of back EMF to voltage is not a direct measure of running torque. Running torque is influenced by the load on the motor and the current flowing through the armature.

Conclusion:

In conclusion, the ratio of back EMF to the applied voltage of a DC motor is an indication of its efficiency. A higher ratio implies that the motor is converting a greater portion of the electrical input into useful mechanical output with fewer losses. Understanding this relationship is crucial for analyzing the performance and efficiency of DC motors in various applications.