Maximum running torque of induction motor is obtained when | Electrical MCQ | Examoogle

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Maximum running torque of induction motor is obtained when

A) $R_2 = X_2$

B) $R_2 = sX_2$

C) $R_2 = s/X_2$

D) $sR_2 = X_2$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalMachine

Option B

$R_2 = sX_2$

Quick Summary:

The maximum torque (also known as breakdown torque or pull-out torque) in a 3-phase induction motor is obtained when the rotor resistance per phase equals the rotor standstill reactance per phase multiplied by the slip. This condition is derived by differentiating the torque equation with respect to slip $s$ and setting the result to zero.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$T = \frac{3}{2\pi N_s} \cdot \frac{s E_2°2 R_2}{R_2°2 + (sX_2)^2}$ — Torque equation of a 3-phase induction motor

$s_m = \frac{R_2}{X_2}$ — Slip at which maximum torque occurs

$T_{max} = \frac{3}{2\pi N_s} \cdot \frac{E_2°2}{2 X_2}$ — Maximum (breakdown) torque expression

⚙️ Working Principle

The torque produced in an induction motor depends on the rotor resistance, rotor standstill reactance, and slip. At starting or low speeds, the inductive reactance of the rotor dominates the impedance, phase angle between rotor current and flux becomes large, reducing torque production. As slip changes, the maximum torque occurs when the maximum power transfer theorem condition is satisfied, i.e., when rotor resistance $R_2$ equals the effective rotor reactance $sX_2$ .

📌 Key Points

▸
Maximum running torque is independent of rotor resistance $R_2$ , but the slip $s_m$ at which maximum torque occurs is directly proportional to $R_2$ .
▸
To obtain maximum torque at starting ( $s = 1$ ), the rotor resistance must equal the standstill rotor reactance ( $R_2 = X_2$ ).
▸
Adding external resistance to the rotor circuit of a slip-ring induction motor increases starting torque without changing the peak magnitude of maximum torque.

📄 Additional Information

▸
Standard torque-slip characteristic shows two distinct regions: stable low-slip region (linear) and unstable high-slip region.
▸
Option A ( $R_2 = X_2$ ) represents the condition for maximum torque at starting when $s = 1$ .
▸
Option C ( $R_2 = s/X_2$ ) and Option D ( $sR_2 = X_2$ ) are mathematically incorrect formulations.

📊 Diagram / Illustration

✅

B is correct — Maximum torque occurs when rotor resistance per phase equals slip times standstill rotor reactance ( $R_2 = sX_2$ ).

Core Concepts Used

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3-Phase Induction Motor Torque Equation Maximum Torque Condition (Breakdown Torque) Rotor Resistance Control & Torque-Slip Curve

💡 EXAM TIP

Always distinguish between maximum running torque condition ( $R_2 = sX_2$ ) and maximum starting torque condition ( $R_2 = X_2$ , where $s=1$ ). Questions frequently trick candidates on this exact distinction.

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