DC MOTOR-Voltage,Power and max power Equation

VOLTAGE EQUATION OF D.C. MOTOR 
Let in a d.c. motor (See Fig. 4.3), 

v=applied voltage 

Eb=back e.m.f. 

Ra=armature resistance 

Ia=armature current 

Since back e.m.f. Eb acts in opposition to the applied voltage V,the net voltage across the 

armature circuit is V — Eb. The armature current Ia is given by ; 


Ia=V - Eb/Ra

OR V=Eb+IaRa



This is known as voltage equation of the d.c. motor. 





4.6 POWER EQUATION 

If eq. ( above is multiplied by la throughout, we get, 

VIa= Eb1a+Ia.IaRa 

This is known as power equation of the d.c. motor. 

Vla = electric power supplied to armature (armature input) 

Ebla =*power developed by armature (armature output) 

IaRa= electric power wasted in armature (armature Cu lass) 

Thus out of the armature input, a small portion (about 5%) is wasted as Ra and the remainig 
portion Ebla is converted into mechanical power within the armature. 



 

CONDITION FOR MAXIMUM POWER 
The mechanical power developed by the motor is Pm= EbIa 

Pm = vIa-(Ia.IaRa) 

Now, 

Since, V and Ra are fixed, power developed by the motor depends upon armature current. For 

maximum power, dPm/dIa should be zero. 

 dPm/dIa=V-2IaRa=0
Now, 

IaRa=V/2

V=Eb+IaRa =Eb+v/2 
Eb=V/2 

Hence mechanical power developed by the motor is maximum when back e.m.f. is equal to half 

the applied voltage. 

Limitations : In practice, we never aim at achieving maximum power due to the following 

The armature current under this condition is very large — much excess of rated current


 of the machine.