Condition for Maximum Power of DC Motor

The DC motor is most suitable for loads that demand a higher starting torque. When DC voltage is applied to the armature, the motor is at a standstill, and no back EMF is induced across the armature. As a result, the motor draws a large current from the supply source and delivers higher starting torque as torque is proportional to the armature current.

separately excited DC motor

The voltage applied to the armature overcomes the back EMF, and voltage drops in the armature winding. As per Kirchhoff’s voltage law, all the voltages around a closed loop in a circuit are equal to zero.

dc motor voltage equation

The equation (1) is called the voltage equation of the DC motor. 

Power Equation of DC Motor

The power developed by motor can be determined by multiplying the voltage applied (V) to armature current(Ia). By Multiplying both sides of equation(1) by Ia, we get the power equation of the DC Motor.

dc motor power equation

Thus, the efficiency of the DC motor depends on the back EMF (Eb), and the motor has higher efficiency if the back EMF is higher.

Condition for Maximum Power

dc motor maximum power and its derivation

Thus, the motor will deliver maximum power when the back EMF is equal to half of the applied armature voltage. 

However, this condition can not be realized. If the back EMF is half of the applied armature voltage, the motor will draw more current than its rated current, and the efficiency of the motor will be below 50 percent.

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