## Slip :

####
The slip is defined as the difference between the synchronous speed ( N_{s} ) and the actual speed of the motor ( N ), expressed of fraction of synchronous speed.

#### Thus slip,

####
**S = N**_{s}
– N / N_{s}

_{s}– N / N

#### Percentage slip,

####
**% S = ( N**_{s}
– N / N_{s} ) ×** 100**

_{s}– N / N

_{s}) ×

### Check out more about slip here - Slip in Induction Motor

## Rotor Frequency :

#### The relation between synchronous speed, supply frequency and the number of stator poles is given by,

####
**f = N**_{s} P / 120 Hz ...(1)

_{s}P / 120 Hz

####
When the rotor rotates at a speed ' N ' then the rotor conductor cut the rotating magnetic field at the relative speed i.e., N_{s }-
N. The frequency of the rotor induced emf or current ' f_{r }' can expressed as

####
**f**_{r}
=
( N_{s} – N ) P / 120 Hz ...(2)

_{r}= ( N

_{s}– N ) P / 120 Hz

#### Dividing equation ( 2 ) by ( 1 ), we get

### Therefore,

####
f_{r }= s f in running condition

####
So rotor frequency in running condition is slip times the supply frequency.

At start, N = 0 and slip = 1, Hence f_{r }= f

Under normal running condition, the rotor frequency is very small as slip is very small.

_{r }= f

## Rotor Induced EMF :

#### When the rotor is stationary or Stand still i.e., slip = 1, the emf induced in the rotor is maximum. This is due to the rate of cutting the flux by rotor is maximum as the relative speed between rotor and rotating magnetic field is maximum.

####
As rotor gains speed, the relative speed decreases. This reduces the magnitude of induced emf in the rotor, proportionality. The relative speed is ' N_{s }-
N ' rpm, when motor is running at speed ' N ' rpm.

### At Stand still :

#### Rotor induced emf / phase at stand still,

####
**E**_{2r} α
N_{s} ( Since N = 0 start )

_{2r}α N

_{s}

### Under Running Condition :

#### Rotor induced emf / phase under running condition,

####
**E**_{2r} α**
( N**_{s} – N )

_{2r}α

_{s}– N )

#### Dividing equation ( 1 ) by ( 2 ), we get

#### Therefore,

#### Rotor induced EMF under running condition will be slip times the rotor induced EMF at stand still.

## Rotor Reactance :

####
The rotor reactance depends upon the frequency. At slip s, the frequency of the rotor induced emf f_{r }= s f

Let,

_{r }= s f

####
L_{2} = Inductance of the rotor per phase

### At standstill :

####
**f**_{r }= f

_{r }= f

### Hence,

#### Rotor reactance / phase at stand still,

####
X_{2 }= 2 π f_{r} L_{2 }= 2 π f L_{2}

### Under Running Condition :

####
f_{r }= s f

####
Hence

#### Rotor reactance / phase under running condition,

####
####
X_{2r }= 2 π f_{r} L_{2 }= 2 π sf L_{2 }

Therefore,

####
X_{2r }= 2 π f_{r} L_{2 }= 2 π sf L_{2 }

####
####
X_{2r }=
s X_{2}

####
Rotor reactance under running condition will be slip times the rotor reactance at stand still.

####
X_{2r }=
s X_{2}

#### Rotor reactance under running condition will be slip times the rotor reactance at stand still.

## Rotor Resistance :

#### Let,

####
R_{2} = Stand still rotor resistance / phase

####
####
Rotor resistance is independent of frequency and hence rotor resistance remains same as ' R_{2} ' Ω / phase at stand still and in running condition.

####
Rotor resistance is independent of frequency and hence rotor resistance remains same as ' R_{2} ' Ω / phase at stand still and in running condition.

## Rotor Impedance :

#### The rotor impedance / phase at stand still and under running condition is given by

####
**Z**_{2} = R_{2}
+ JX_{2}

_{2}= R

_{2}+ JX

_{2}

####
= √ ( R_{2} + X_{2} )^{2} at stand still

### And

####
**Z**_{2r} = R_{2}
+ J sX_{2}

_{2r}= R

_{2}+ J sX

_{2}

## 1 Comments

Yes sir I was check it yeah absolute correct fraction

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