Power Equation of a D.C. Motor

Power Equation of a D.C. Motor

The voltage equation of a d.c. motor is given by,

V = E_b + l_a R_a

Multiplying both sides of the above equation by I_a we get,

V I_a =  E_b l_a + I_a² R_a

This equation is called power equation of a d.c. motor.

V I_a = Net electrical power input to the armature measured in watts.

I_a² R_a = Power loss due to the resistance of the armature called armature copper loss.

So difference between V I_a and I_a² R_a i.e. Input Losses gives the output of the armature.

So E_b I_a is called electrical equivalent of gross mechanical power developed by the armature. This is denoted as P_m.

Power input to the armature - Armature copper loss = Gross mechanical power developed in the armature

1. Condition for Maximum Power

For a motor from power equation it is known that.

Key Point: This is practically impossible to achieve as for this E_b, current required is much more than its normal rated value. Large heat will be produced and efficiency of motor will be less than 50 %.

Review Questions

1. Derive the power equation for a d.c. motor.

2. Derive the condition for maximum power for a d.c. motor.