Question

A wound rotor induction motor runs with a slip of 0.05 when developing full load torque. Its rotor resistance is 0.45 Ω per phase. If an external resistance of 0.50 Ω per phase is connected across the slip rings, what is the slip for full torque?
1. 0.03
2. 0.06
3. 0.09
4. 0.1

Answer 1

Correct Answer - Option 4 : 0.1

Concept:

Rotor resistance method of speed control:

Under load condition torque approximately

T ∝ (sV12) / (R2 + Re)

• In this method, some external resistance is inserted under the load conditions.
• Then the slip of the induction motor increases to maintain the load torque constant.
• As slip is increased, the speed of the motor will be reduced to below the rated speed.
• In this method, the motor acts as a constant torque variable power drive.

 

For torque constant(T = k)

\(\frac{{{{\bf{s}}_1}}}{{{{\bf{R}}_2}}} = \frac{{{{\bf{s}}_2}}}{{{{\bf{R}}_2} + {{\bf{R}}_{\bf{e}}}}}\)

Calculation:

For induction motor, the torque in rotor resistance control methods is given as

\({\rm{{\rm T}}} = \frac{{{K_t}s}}{{{R_2}}}\)

For full load torque \(s\; \propto \;{R_2}\)

\(\begin{array}{l} {s_2} = \frac{{{R_2} + {R_{ext}}}}{{{R_2}}} \times {s_1}\\ = \frac{{0.45 + 0.5}}{{0.45}} \times 0.05 \end{array}\)

= 0.1055