For improve the power factor of a single phase motor, the capacitor should be connected in

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parallel to the motor

Explanation: To improve the power factor of a single-phase induction motor, a capacitor is connected in parallel with the motor terminals. This arrangement provides a leading current that offsets the lagging inductive current drawn by the motor, thereby reducing the overall phase angle between voltage and current.

Working Principle: Single-phase motors are inherently inductive due to their stator windings, which cause the current to lag behind the voltage, resulting in a low power factor. By connecting a capacitor in parallel, the capacitor draws a leading reactive current ($I_C$). This current cancels out a portion of the magnetizing component of the motor's lagging current ($I_L sin \phi_m$), effectively decreasing the total reactive power drawn from the source.

Key Formulas: $Q_C = V^2 \omega C$ — Reactive power supplied by the capacitor; $PF = \cos(\phi) = \frac{P}{\sqrt{P^2 + Q^2}}$ — Definition of Power Factor

Key Points: Parallel connection is standard for power factor correction (static compensation).; It reduces the line current, thereby minimizing copper losses ($I^2R$) in the transmission lines.; The capacitor does not change the motor's internal performance, only the load seen by the source.; Over-correction can lead to a leading power factor, which may cause voltage rise at the motor terminals.

Advantages: Reduces total kVA demand from the source; Decreases distribution line losses; Improves voltage regulation at the load end

Disadvantages: Risk of over-correction leading to leading power factor; Additional capital cost for capacitor installation

Applications: Industrial induction motor installations; Utility distribution transformers; Power grid stability management

Additional Info: Series capacitors are typically used for voltage regulation in long transmission lines to compensate for line reactance, not for power factor correction of loads.. Option A is incorrect because a series capacitor would introduce additional impedance and potentially lead to resonance with motor leakage reactance.

Answer: B is correct — Connecting a capacitor in parallel provides the necessary reactive VARs to neutralize the inductive lagging current of the motor, thus improving the overall power factor.

Exam Tip: In exams, remember that series capacitors are for voltage stability in lines, while parallel capacitors are for load power factor correction.

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