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The correct answer is Option A: Only 1 is true. Statement 1 is correct because the slip at maximum torque is determined by maximizing the rotor power output (or air-gap power), which is analogous to applying the Maximum Power Transfer Theorem to the Thevenin equivalent circuit of the induction motor. Statement 2 is incorrect because the standard relationship between torque ($T$), power ($P$), and angular velocity ($\omega$) is $T = \frac{P}{\omega}$, not $T = \frac{\omega}{P}$.

Step-by-Step Solution & Concepts:
Statement 1 is correct because the slip at maximum torque is determined by maximizing the rotor power output (or air-gap power), which is analogous to applying the Maximum Power Transfer Theorem to the Thevenin equivalent circuit of the induction motor. Statement 2 is incorrect because the standard relationship between torque ($T$), power ($P$), and angular velocity ($\omega$) is $T = \frac{P}{\omega}$, not $T = \frac{\omega}{P}$.

Working Principle: The induction motor rotor circuit can be modeled as a Thevenin equivalent. The maximum power transfer occurs when the rotor resistance referred to the stator ($R'_r/s$) equals the magnitude of the equivalent stator impedance. By equating these, we derive the expression for slip at maximum torque.

Key Formulas: $T = \frac{P}{\omega}$; $s_{mT} = \frac{R'_r}{\sqrt{R_{th}^2 + (X_{th} + X'_r)^2}}$

Key Points: Maximum power transfer theorem dictates that maximum power is transferred when the load resistance equals the source resistance.; Torque is the ratio of mechanical power to angular speed, $T = \frac{P}{\omega}$.; Slip at maximum torque is independent of stator supply voltage magnitude.

Additional Info: The variable $\omega$ represents angular speed in rad/sec, not to be confused with any other notation.. The second statement misrepresents the fundamental physics equation $P = T \omega$ by inverting the terms.

Answer: A is correct — Only the first statement regarding the application of the maximum power transfer theorem is technically accurate.

Exam Tip: Always verify dimensional consistency in equations; since power is in Watts ($J/s$) and torque is in $N\cdot m$, $T = P/\omega$ correctly results in units of $N\cdot m$.

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Option B: Only 2 is true

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Option C: Both 1 and 2 are true

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Option D: Both 1 and 2 are not true

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