**01. Lenz’s law of motor-**

*Lenz’s law of motor is the principle theory of motor *

A current carrying conductor will experience a force when placed in a magnetic field. The conductor can be any metal—iron, copper, aluminum, and so on.

*F = IBL sin θ*

where

F = force on the conductor (in Newtons)

I = current through the conductor (in amperes)

B = magnetic flux density (in gauss)

L = length of the wire (in meters)

θ = angle between the magnetic field and current

*The direction of the force is perpendicular to both the magnetic field and the current.*

**02. torque & force relationship in motor-**

Electric motor torque is directly proportional to the force on the armature wires.

*T = Kt Ia φ, *

where

T = motor torque

Kt = a constant based on the motor construction

Ia = armature current

φ = magnetic flux

**03. Faraday’s laws of electromagnetic induction in motor**

As the armature of motor is rotating in the magnetic field of field winding, according Faraday’s laws of electromagnetic induction a certain voltage also induced in the armature winding.

*EMF = KeφS*

where

EMF = voltage generated by the turning motor

Ke = a constant based on motor construction

φ = magnetic flux

S = speed of motor (rpm)

This induced voltage will try to cancel out the line voltage, that is it will be of opposite polarity.

The actual voltage available to the armature is the line voltage

minus the CEMF:

**04. back EMF equqtion in motor**

*VA = Vln – CEMF*

where

Va = actual voltage available to the armature

Vln = line voltage supplied to the motor

CEMF = voltage generated within the motor

We can not directly measure Va with a voltmeter because it is an effective voltage inside the armature. However, there is physical evidence that the CEMF exists because the armature current is also reduced

*Ia = (Vln – CEMF)/Ra*

where

Ia = armature current

Vln = line voltage to the motor

Ra = armature resistance

CEMF = voltage generated within the motor

The actual relationship between motor speed and CEMF follows

*S = CEMF/(Kφ)*

where

S = speed of the motor (rpm)

CEMF = voltage generated within the motor

KE = a motor constant

φ = magnetic flux

*P = TS*

where

P = power

T = torque

S = motor speed

1 hp = 33,000 (ft.lb/min)

Soon I will complete this Insha Allah