**The difference between the rotor speed (N) and the rotating magnetic flux speed (N**

_{s}) is called slip.The

*induction motor slip*is usually expressed as a percentage of synchronous speed (N

_{s}) and is represented by symbol

**s**.

Mathematically, Percentage slip, % s = [(N

_{s}– N)/N

_{s}] x 100

or Fractional slip, s = (N

_{s}– N)/N

_{s}

The difference between synchronous speed and rotor speed is called slip speed

i.e. Slip speed = N

_{s}– N

The value of

**induction motor slip**at full load varies from about 6% for small motors to about 2% for large motors.

# Importance of Induction Motor Slip

Slip plays an important role in the operation of the induction motor.

**The torque produced by the induction motor is directly proportional to induction motor slip. At no-load induction motor requires small torque to meet with the frictional, iron and other losses, therefore slip is small.
When the motor is loaded, greater torque is required to drive the load, therefore, slip increases and rotor speed decreases slightly. Thus induction motor slip adjusts itself to such a value so as to meet the required driving torque. **

At standstill N = 0 hence s = 1 whereas at N = N

_{s}, s = 0 (imaginary condition).

## Induced EMF in Rotor

E_{2r} = sE_{2}

Where E_{2} = Induced EMF per phase at standstill.

E_{2r }= Rotor induced EMF per phase in running condition.

At standstill s = 1 hence E_{2r} = E_{2} whereas at N = N_{s}, s = 0, E_{2r} = 0.

**Thus rotor induced EMF fluctuates between 0 and E _{2} for the rotor speeds between N = N_{s} and N = 0.**

## Frequency of Induced EMF in Rotor

The expression for frequency of induced EMF in the rotor is:

**f _{r} = sf_{1}**

i.e. rotor EMF frequency = fractional slip x supply frequency

**At standstill, induction motor slip s is 1, hence the frequency of induced EMF in the rotor of the induction motor is same as that of supply frequency and reduces with increase in speed (due to the reduction in slip).**

## Rotor Resistance

There is no effect of rotor induced EMF frequency on its resistance. Hence the rotor resistance remains constant irrespective of the speed of the induction motor.

## Rotor Reactance

**Let X _{2} be the rotor reactance per phase at standstill**. The rotor frequency at standstill is f

_{r}= f

_{1}.

Therefore, X

_{2}= 2πf

_{1}L

_{2}ohm/phase

In the running condition the frequency of rotor voltage is f

_{r }= sf

_{1}. Hence rotor reactance in the running condition X

_{2r}is given by,

X

_{2r}= 2πf

_{r}L

_{2}= 2πsf

_{1}L

_{2}= s (2πf

_{1}L

_{2}) = sX

_{2}

**X**

_{2r}= sX_{2}.**At standstill, induction motor slip s is 1, hence reactance of rotor of the induction motor is same as reactance of rotor at standstill and reduces with increase in speed (due to the reduction in slip).**

## Rotor Impedance

The rotor impedance per phase at standstill is given by,

Z_{2 }= (R_{2}^{2} + X_{2}^{2})^{1/2} ohm/phase

The rotor impedance per phase at running condition is given by,

Z_{2r} = (R_{2}^{2} + sX_{2}^{2})^{1/2} ohm/phase

Where R_{2} = Rotor resistance per phase

X_{2} = Reactance of the rotor winding per phase at standstill.

## Rotor Power Factor

At standstill, the rotor power factor is given by,

cos φ_{r} = R_{2}/Z_{2} = R_{2}/(R_{2}^{2} + X_{2}^{2})^{1/2}

At running condition, the rotor power factor is given by,

cos φ_{2r} = R_{2}/Z_{2r} = R_{2}/[R_{2}^{2} + (sX_{2})^{2}]^{1/2}

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