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The maximum torque of a 3-phase induction motor under running conditions is

The maximum torque of a 3-phase induction motor under running conditions is **Inversely proportional to the Rotor reactance at standstill**.

The maximum torque of an induction motor is given by the following equation:

\(T_{max} = K \cdot \frac{E_2^2}{2X_2}\)

where:

K is a constant that depends on the motor design and operating conditions

E2 is the effective voltage induced in the rotor (proportional to the stator voltage and the slip)

X2 is the rotor reactance

T{max} is the maximum torque.

From this equation, we can see that the maximum torque is directly proportional to the square of the effective voltage induced in the rotor and inversely proportional to the rotor reactance. This means that as the rotor reactance decreases, the maximum torque increases.

We can also see that the maximum torque is not dependent on the rotor resistance $R_2$, but the slip at which it occurs is dependent on the value of rotor resistance $R_2$. This is because the slip at maximum torque is given by:

\(s_{max} = \frac{R_2}{X_2}\)

As we can see, the slip at maximum torque is inversely proportional to the rotor reactance and directly proportional to the rotor resistance.

Therefore, we can conclude that the maximum torque of a 3-phase induction motor is inversely proportional to the rotor reactance, and the slip at which it occurs is dependent on both the rotor resistance and reactance.

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