The corresponding poly-phase induction motor circuit is shown in Fig. 24, where

V_{1} = applied voltage per phase

R_{1} = stator resistance/phase

R_{2} = rotor resistance/phase

X_{1} = stator leakage reactance/phase

X_{2} = rotor standstill leakage reactance/phase

K = turn-ratio of secondary to primary

R_{0} = no-load resistance/phase

X_{0} = no-load reactance/phase

Fig. 24. Equivalent circuit of an induction motor

It is illustrated in the figure that when the circuit is transferred to the left, the circuit and calculations are much simpler because of the negligible inaccuracy. Such a process is called induction motor equivalent circuit as the approximate value.

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__Maximum Power Output (shown in figure no. 25)__

In order to obtain the maximum power output, let’s differentiate the mentioned equation by equating the first derivative to 0.

By the mentioned equation we can say that gross mechanical power output will maximum when the standstill leakage impedance is equal to the equivalent load resistance R_{L }of the motor Z_{01}.

**Example **

*In a 3-phase induction motor maximum torque occurs at a slip of 15 per cent. The equivalent secondary resistance of the motor is 0.07 Ω/phase. If the gross power output is 9.5 II W. Calculate.-*

*(i) Equivalent load resistance, *

*(ii) Equivalent load voltage, and *

*(iii)Current at this slip. *

**Solution**

Slip at maximum torque, s = 15 per cent

The equivalent secondary resistance of the motor,

R_{2} = 0.07 Ω/phase

Gross power output, P_{g} = 9.5 kW or 9500 W

**Equivalent load resistance, RL:**

We know that

= (please calculate the value)

**Equivalent load voltage, V:**

V is a fictitious voltage drop which is equal to the consumption in the secondary load connected, i.e., rotor, V = I_{2}R_{L}

But, gross power, Pg =

= please calculate the value

**Equivalent load current:**