V curve drawn between

Question

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Option A: Field - Armature current

Explanation & Concepts:
The V-curve of a synchronous motor represents the variation of armature current ($I_a$) as a function of field excitation current ($I_f$) at a constant output power. The curve shape resembles the letter 'V' because the armature current is minimum at unity power factor and increases as the motor becomes either over-excited (leading power factor) or under-excited (lagging power factor).

Working Principle: In a synchronous motor, the armature current $I_a$ is determined by the vector sum of the supply voltage $V$ and the back EMF $E_b$. By varying the field current $I_f$, we change the magnitude of $E_b$. At a specific $I_f$, the back EMF matches the supply voltage such that $I_a$ is in phase with $V$, resulting in unity power factor and minimum armature current.

Key Formulas: $I_a = \frac{V - E_b}{Z_s}$ — fundamental relationship between voltage, back EMF, and synchronous impedance.; $E_b \propto \Phi \cdot N$ — back EMF is directly proportional to flux, which depends on field current $I_f$.

Key Points: Minimum point of the V-curve corresponds to unity power factor (cos φ = 1).; Left side of the V-curve (under-excited) corresponds to lagging power factor.; Right side of the V-curve (over-excited) corresponds to leading power factor.; The inverted V-curve represents power factor vs field current.

Advantages: Enables simple control of power factor in industrial plants.; Provides visual identification of excitation states.

Disadvantages: High variations in field current can cause instability if not regulated.; Requires complex control circuitry for automatic power factor correction.

Applications: Synchronous Condensers for voltage regulation.; Power factor improvement in large industrial power systems.

Additional Info: The term 'V-curve' strictly refers to $I_a$ vs $I_f$, whereas 'Inverted V-curve' refers to $cos(\phi)$ vs $I_f$.. Option B, C, and D are incorrect because they describe power factor relationships or load characteristics rather than the defined V-curve relationship.

Answer: A is correct — The V-curve is specifically defined as the plot of armature current $I_a$ against the field excitation current $I_f$.

Exam Tip: Always remember: V-curve is $I_a$ vs $I_f$ (Looks like V), Inverted V-curve is $cos(\phi)$ vs $I_f$ (Looks like upside-down V).

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Option B: Voltage - Load factor

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Option C: Power factor - Field current

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Option D: Power factor - Voltage

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