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Electrical Machines

Voltage and Power Equations of DC Motor | Condition of Maximum Power

  • Categories Electrical Machines, Basic Electrical, DC Generator, DC Motor, Measurement
dc motor voltage and power equations
dc%2Bmotor%2Bvoltage%2Band%2Bpower%2Bequations
In this post, we will look at the voltage and power equation of a dc motor and the condition for maximum power in a dc motor.

Table of Contents

  • Voltage Equation of a DC Motor
  • Power Equation of DC Motor
    • Condition for Maximum Power
    • Related Articles

Voltage Equation of a DC Motor

The voltage V applied across the motor armature has to

  1. overcome the back emf Eb and
  2. supply the armature ohmic drop IaRa .

voltage%2Bequation%2Bdc%2Bmotor

This is known as voltage equation of a motor.

Back EMF and Its Significance in DC Motor
Working Principle of DC Motor

Power Equation of DC Motor

Now, multiplying both sides of voltage equation by Ia , we get
power%2Bequation%2Bdc%2Bgenerator%2Bdc%2Bmotor
Hence, out of the armature input, some is wasted in I2R loss and the rest is converted into mechanical power within the armature.

The gross mechanical power developed by a motor is
power%2Bequation%2Bdc%2Bgenerator%2Bdc%2Bmotor%2B1saf
It may also be noted that motor efficiency is given by the ratio of power developed by the armature to its input
power%2Bequation%2Bdc%2Bgenerator%2Bdc%2Bmotor%2B2
Obviously, the higher the value of Eb as compared to V, higher the motor efficiency.

Condition for Maximum Power

The gross mechanical power developed by a motor is
gross%2Bmechanical%2Bpower%2Bdc%2Bmotor%2Bdc%2Bgenerator
Differentiating both sides with respect to Ia and equating the result to zero, we get

Thus maximum efficiency of a dc motor occurs when back EMF is equal to half the applied voltage.

Important Points

Thus gross mechanical power developed by a motor is maximum when back EMF is equal to half the applied voltage.

This condition is, however, not realized in practice, because in that case current would be much beyond the normal current of the motor.


Moreover, half the input would be wasted in the form of heat and taking other losses (mechanical and magnetic) into consideration, the motor efficiency will be well below 50 percent.

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    1 Comment

  1. peter
    November 13, 2019
    Reply

    really helpfull , thanks alot.

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