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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

    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

    power%2Bequation%2Bdc%2Bgenerator%2Bdc%2Bmotor

    Now, multiplying both sides of voltage equation by Ia , we get

    Hence, out of the armature input, some is wasted in I2R loss and the rest is converted into mechanical power within the armature.

    power%2Bequation%2Bdc%2Bgenerator%2Bdc%2Bmotor%2B1saf
    power%2Bequation%2Bdc%2Bgenerator%2Bdc%2Bmotor%2B2

    The gross mechanical power developed by a motor is

    It may also be noted that motor efficiency is given by the ratio of power developed by the armature to its input

    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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