# Torque And Speed Equations Of Dc Motor

Before analysing the various characteristics of motors, let us revise the torque and speed equations are applied to various types of motors.

**. ^{.}.** T α Φ I

_{a }from torque equation.

This is because, 0.159(PZ)/A is a constant for a given motor.

Now Φ is the flux produced by the field winding and is proportional to the current passing through the field winding.

Φ α I_{field}

But for various types of motors, current through the field winding is different. Accordingly torque equation must be modified.

For a d.c. shunt motor, I_{sh }is constant as long as supply voltage is constant. Hence Φ flux is also constant.

**. ^{.}. **T α Ia for shunt motors

For a d.c. series motor, I

_{se }is same as I

_{a}. Hence flux Φ is proportional to the armature current I

_{a}.

**. ^{.}. **T α I

_{a }α I

_{a}

^{2}

_{ }for series motors.

Similarly as E_{b }^{ }= (ΦPNZ)(60A), we can write the speed equation as,

E_{b }α ^{ }Φ N

**. ^{.}. **N α E

_{b}/Φ

But V = E

_{b }+ I

_{a }R

_{a }neglecting brush drop

**.**E

^{.}._{b }= V – I

_{a }R

_{a}

**.**Speed equation becomes,

^{.}.N α (V-I

_{a }R

_{a})/Φ

So for shunt motor as flux is constant,

**.**N α V – I

^{.}._{a }R

_{a}

While for series motor, flux Φ is proportional to I_{a}.

These relations play an important role in understanding the various characteristics of different types of motors.

__1.1 Speed Regulation__

The speed regulation for a d.c. motor is defined as the ratio of change in speed corresponding to no load and full load condition to speed corresponding to full load.

Mathematically it is expressed as,