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

V = E

_{b }+ I_{a }R_{a } Multiplying both sides of the above equation by I

_{a }we get, This equation is called power equation of a d.c. motor.

VI

_{a }= Net electrical power input to the armature measured in watts. I

_{a}_{}^{2}R_{a }_{ }= Power loss due the resistance of the armature called armature copper loss. So difference between VI

_{a }and I_{a}^{2}R_{a }_{ }i.e. input - losses gives the output of the armature. So E

_{b }_{ }Ia 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.

__1.1 Condition for Maximum Power__

For a motor from power equation it is known that,

P

_{m }= Gross mechanical power developed = E_{b }_{ }Ia_{ }= VIa - I

_{a}

^{2}Ra

For maximum P

_{m}, dP_{m}/dI_{a}= 0**.**0 = V - 2I

^{.}._{a}Ra

**.**I

^{.}._{a }= V/2Ra i.e. I

_{a}Ra = V/2

Substituting in voltage equation,

V = E

_{b }_{ }+ I_{a}Ra = E_{b }_{ }+ (V/2)**.**E

^{.}._{b }

_{ }= V/2 .................Condition for maximum power

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

__Related articles :__**D.C. Motors****Direction of Rotation of D.c. Motor****Significance of Back E.M.F.****Torque Equation of a D.C. Motor**

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