The equivalent circuit of a 3 phase induction motor is shown in the Fig.1.

Fig. 1 Equivalent circuit of a 3 phase induction motor |

All the values shown are per phase values. The circuit is similar to series R-L circuit. The reactance X

I

_{1e }is fixed while the total resistance R_{1e }+ (R_{2}**'**(1-s)/s) is variable. This is because the slip s varies as load varies. The voltage across the parallel exciting branch is V_{1}. Hence we can write the expression for the rotor current referred to stator as,I

_{2r}**'**= V_{1}/√**(**(R_{1e }+ R_{L })^{2}+ X_{1e}^{2}**)** Where R

_{L}**'**= R_{2}**'**(1-s)/s = Variable equivalent load resistance R

_{1e }= R_{1 }+ R_{2}**'**= Equivalent resistance of motor referred to stator X

_{1e }= X_{1 }+ X_{2}**'**= Equivalent reactance of motor referred to stator**.**I

^{.}._{2r}

**'**= I

_{max}sin ....................(1)

where sinΦ = X/Z = X

_{1e}/√**(**(R_{1e }+ R_{L}**'**_{ })^{2}+ X_{1e}^{2}**)** and I

_{max}= V_{1}/X_{1e } The I

_{2r}**'**will be at its maximum when R_{1e }+ R_{L}**'**= 0 i.e., there exists an ideal short circuit. Hence current I_{max}is called ideal short circuit current of an induction motor. The equation (1) represents equation of a circle with as its diameter. Thus locus of extremely of I

_{2r}**'**is a circle, as shown in the Fig.2.Fig. 2 Circle diagram of I_{2r}' |

But the total stator current I

_{1}per phase is a vector addition of current I_{o}and I_{2r}**'**. I

_{1}= I_{o}+ I_{2r}**'**....... Vector addition For and induction motor, I

Ī

_{o}has a fixed value and phase angle Φ_{o}which is decided by its active component and magnetising component I_{m}.Ī

_{o}= Ī_{c}+ Ī_{m} As I

_{o}has fixed magnitude and phase, the locus of extremities of I_{1}, which is I_{o}+ I_{2r}**'**is also a circle with a diameter still as V_{1}/X_{1e}. The only charge will be that the diameter V_{1}/X_{1e }will no longer be along X-axis i.e. current axis but will get shifted at the tip of the I_{o}phasor. All the I_{2r}**'**phasors are to be drawn from I_{o}phasor to get I_{1}, as has fixed magnitude and phase angle Φ_{o}.**Key Point**: Thus the current locus for a stator current is also a semicircle which is truly called circle diagram of a three phase induction motor. This diagram once obtained can be used to predict the performance of an induction motor under variable load conditions.

Let us see, how to obtain the data for plotting the circle diagram.

**Obtaining Data to Plot Circle Diagram**The data required to draw the circle diagram is obtained by conducting two testes which are,

1. No load test or open circuit test

2. Blocked rotor test or short circuit test

__Related articles :__**Circle Diagram : Introduction****Circle Diagram for a Series R-L Circuit****No Load Test****Blocked Rotor Test****Construction of Circle Diagram****Load Tets on Three Phase Induction Motor**

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