P

_{in }= total input of a machine
P

_{cu }= variable losses
P

_{i }= constant losses
then P

In case of a d.c. generator the output is given by,

P

P

I

The efficiency is maximum, when the denominator is minimum. According to maxima-minima theorem,

Thus for the maximum efficiency, the condition is,

At maximum efficiency,

I

At maximum efficiency,

I

Torque Equation of a D.c. Motor

Characteristics of D.C. Shunt Motor

Applied Voltage Control

Four Point Starter

_{in }= P_{out }+ P_{cu }+ P_{i }_{ }__1.1 Condition for Maximum Efficiency__

P

_{out }= VIP

_{cu }= variable losses = I^{2}R_{a }= I^{2}R_{a }I

_{a }= I .................. neglecting shunt field currentThe efficiency is maximum, when the denominator is minimum. According to maxima-minima theorem,

Thus for the maximum efficiency, the condition is,

**Variable losses = Constant losses**__1.2 Current at Maximum Efficiency__

From the condition of maximum efficiency, the current through the d.c. machine at the time of of maximum efficiency can be obtained.

**For shunt machines**: The I

_{sh }is constant and the loss VI

_{sh }is treated to be the part of constant losses. The variable losses are I

_{a}

^{2}

_{ }R

_{a}.

I

_{a}^{2}_{ }R_{a }= P_{i }= (Stray + shunt field losses)
This is the armature current at maximum efficiency. Neglecting I

_{sh}, I_{a}= I_{L}^{}is the line current of the machine.**For**

**series machines**: The current through series field is same as armature current which is same as line current. Hence the constant losses are only mechanical losses while the variable losses are the copper losses in armature as well as series field winding due to the armature current.

I

_{a}^{2}_{ }(_{ }R_{a }+_{ }R_{se}) = P_{i }= Mechanical losses**See solved examples on eff and power loss of dc motor**

__Related Articles :__Characteristics of D.C. Shunt Motor

Applied Voltage Control

Four Point Starter

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