Since DC motor is a machine it must have some losses during its operation. As the current flows through armature windings and field windings, there are certain copper losses. Since the current alters its direction continuously in the armature winding, there are hysteresis and eddy current losses in the armature core. We call the hysteresis and eddy current loss collectively as core loss or magnetic loss. A dc motor is a dynamic machine, hence there is a frictional loss in the bearings. For the same reason, there is a windage loss in the air gap between rotor and stator. Both frictional and windage loss are mechanical losses.

## Losses of DC Motor

Hence a dc motor has three kinds of loss and they are,

- Copper Losses
- Armature Copper Loss
- Field Copper Loss

- Iron Losses
- Hysteresis Loss
- Eddy Current Loss

- Mechanical Losses
- Friction Loss
- Windage Loss

### Power of DC Motor

In a dc motor, the armature develops the mechanical power and the mathematical expression of the approximate mechanical power is

Where V is the supply voltage, I_{a} and R_{a} are armature current and armature resistance respectively. We refer to this expression as approximate mechanical power since we have neglected here the shunt field current and series field resistance of the motor because both of them are quite small.

Differentiating both sides of the expression with respect to the armature current (I_{a}), we get,

This is the condition of maximum power in the motor. Again, the voltage equation of the dc motor is,

Therefore, at the maximum power condition,

So, when the back emf of the motor becomes half of the supply voltage, the motor delivers maximum mechanical power.

## Efficiency of DC Motor

Let us consider V is the supply voltage to the dc motor. The motor draws current I from its supply mains during its operation. So the input power to the motor is

After copper losses, the armature develops mechanical power,

After friction and windage loss the mechanical power appearing at the shaft of the motor for doing the work is

Where W_{c} is the constant iron loss in the machine. So, the approximate power equation of the motor is

But there are other two losses what we have not considered for simplicity of power equation. These are the copper losses is shunt and series field.

#### Power Equation for Shunt Field DC Motor

Here in shunt dc motor, the supply current (I) has two components. One is armature current (I_{a}) and another is shunt field current (I_{f}).

Now, considering the shunt filed copper loss, we can write the power equation as

Where R_{sh} is the shunt field resistance.

#### Power Equation for Series Field DC Motor

In series field motor, the same supply current flows through armature and series field.

So, by considering the copper loss of the series filed, we can write

Where R_{se} is the shunt field resistance.

Now, in shunt motor, the shunt field current is very tiny with respect to the armature current. Hence we can neglect the copper loss in the shunt field.

Again, in a series motor, the series field resistance is quite low with respect to the armature resistance. Hence, here also we can neglect the copper loss of the series field.

#### Approximate Power Equation for Compounded Field DC Motor

A compounded wound dc motor there are both shunt and series field. Although we can neglect both series and shunt field copper loss in the machine. Hence, we can write the approximate power equation in this case as

## Efficiency of DC Motor

### Overall Efficiency of DC Motor

The overall efficiency of the dc motor is the ratio of output power to the input power. We also call it as commercial efficiency.

### Electrical Efficiency of DC Motor

This is the ratio of armature power to the input electrical power.

### Mechanical Efficiency of DC Motor

This efficiency determines, how efficiently a motor delivers the armature power to the shaft for doing desired mechanical work by the machine. This is the ratio of output mechanical power to armature power.

### Condition of Maximum Efficiency of DC Motor

If we neglect the shunt field current, we can say supply current is the same as armature current in a dc motor. Hence now we can simplify the expression of overall efficiency of dc motor as

Now the efficiency is maximum when the term under brackets in the above expression is minimum. Again, this condition is satisfied when

The just above expression shows that the efficiency of a dc motor is maximum when

**Copper Loss = Core Loss**