Why locus of the current did not start from the origin (where X and Y-axis start) in the case of circle diagra

Question

Why locus of the current did not start from the origin (where X and Y-axis start) in the case of circle diagram of a three-phase induction motor?

Examoogle · Accepted Answer

The correct answer is Option C: even at no load, IM draw the No-Load Current ($I_o$) due to Mechanical Losses And Iron Losses. The circle diagram of a three-phase induction motor represents the locus of the stator current phasor. It does not start from the origin because, even at no-load, the motor draws a magnetizing current ($I_o$) to establish the rotating magnetic field and to compensate for rotational and iron losses.

Step-by-Step Solution & Concepts:
The circle diagram of a three-phase induction motor represents the locus of the stator current phasor. It does not start from the origin because, even at no-load, the motor draws a magnetizing current ($I_o$) to establish the rotating magnetic field and to compensate for rotational and iron losses.

Working Principle: The stator current $I_s$ is the vector sum of no-load current $I_o$ and the load-dependent rotor current reflected to the stator $I'_r$. Since $I_o$ is always present due to the required magnetizing reactance ($X_m$) and core loss resistance ($R_c$), the current locus is shifted from the origin by the vector $I_o$.

Key Formulas: $I_s = I_o + I'_r$ — Total stator current is the vector sum of no-load and load currents; $I_o = I_w + jI_m$ — No-load current components (Active and Magnetizing)

Key Points: No-load current $I_o$ consists of the magnetizing component ($I_m$) and the active component ($I_w$); The circle diagram is derived from the approximate equivalent circuit; Iron losses and friction/windage losses constitute the power required at no-load; The diameter of the circle is determined by the short-circuit current

Advantages: Graphical representation of motor performance; Easy determination of slip, power factor, and efficiency at various loads

Disadvantages: Requires assumptions (constant rotor resistance) which may not be accurate; Less precise than analytical equivalent circuit calculations

Applications: Performance analysis of induction motors; Predicting torque-slip characteristics

Additional Info: Option A is incorrect because copper losses vary with load and are not the sole reason for the displacement of the locus.. Option B is a general characteristic but does not explain the specific offset in the circle diagram.

Answer: C is correct — The circle diagram locus begins at the vector tip of the no-load current ($I_o$) because the motor must draw this current to overcome magnetizing requirements and mechanical/iron losses.

Exam Tip: Always remember that the 'offset' from the origin in induction motor diagrams is typically attributed to the excitation branch ($R_c$ and $X_m$) of the T-equivalent circuit.

Examoogle · Answer

Option A: due to stator and rotor copper loss

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Option B: because its rotating device

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Option D: All of these

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