### Voltage Equation:

Consider a shunt wound motor shown in Fig.

Let, V = applied voltage

E

I

R

Meanwhile back e.m.f. E

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

Let, V = applied voltage

E

_{b}= back e.m.f.I

_{a}= armature currentR

_{a}= armature resistanceMeanwhile back e.m.f. E

_{b}acts in reverse to the applied voltage V, the net voltage through the armature circuit is V-E_{b.}Now the armature current I_{a}is given by;**I**_{a}= V-E_{b}/_{Ra}**V = E**_{b}+ I_{a}R_{a}**====> (**1**)**This is known as voltage equation of the d.c. motor.

### Power Equation:

If the above Eqn. (1) is multiplied with I

This is said to be a power equation of the d.c. motor.

Where,

VI

E

I

Therefore out of the armature input, a small portion (about 5%) is wasted as I

_{a}throughout, we get,**VI**_{a}= E_{b}I_{a}+ I^{2}_{a}R_{a}This is said to be a power equation of the d.c. motor.

Where,

VI

_{a}= armature input (electric power supplied to armature)E

_{b}I_{a}= armature output (power developed by armature)I

_{a}R_{a}= armature Cu loss (electric power wasted in armature)Therefore out of the armature input, a small portion (about 5%) is wasted as I

^{2}_{a}R_{a}and the remaining portion E_{b}I_{a}is changed into mechanical power within the armature.