In an ac circuit I x sin (Φ) is called the _________ component of the current:

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Examoogle · Accepted Answer

Reactive

Explanation: In an AC circuit, the total current $I$ can be resolved into two orthogonal components: the active (in-phase) component $I \cos(\Phi)$ and the reactive (quadrature) component $I \sin(\Phi)$. The reactive component is responsible for the exchange of energy between the source and the reactive elements (inductors/capacitors) without contributing to active power consumption.

Working Principle: In AC circuits, inductive or capacitive loads create a phase shift $\Phi$ between voltage and current. The component $I \sin(\Phi)$ acts in quadrature (90 degrees) to the voltage, meaning it does not perform useful work in resistive terms. Since average power $P = VI \cos(\Phi)$, the component $I \sin(\Phi)$ results in zero average power consumption, which is why it is often referred to as 'wattless' or 'reactive' current.

Key Formulas: $I_{active} = I \cos(\Phi)$ — The component responsible for real power transfer.; $I_{reactive} = I \sin(\Phi)$ — The component responsible for the magnetic/electric field storage.

Key Points: The reactive component $I \sin(\Phi)$ does not contribute to the real power ($P = VI \cos(\Phi)$).; It is termed 'wattless' because the average power associated with this component is zero.; This current contributes to the reactive power $Q = VI \sin(\Phi)$ measured in VAR (Volt-Ampere Reactive).; High reactive current increases $I^2R$ losses in transmission lines without increasing useful load power.

Advantages: Useful for calculating necessary VAR compensation in power systems.; Essential for understanding phase-angle relationships in phasors.

Disadvantages: High reactive current reduces system efficiency.; Leads to voltage drops and increased thermal loading on transformers and cables.

Applications: Power factor correction using capacitor banks.; Analysis of induction motor performance.; Design of reactive power compensation equipment.

Additional Info: The term 'Wattless' refers to the fact that no 'Watts' (active power) are consumed by this component.. 'Quadrature' refers to the 90-degree phase shift relative to the reference voltage.. Option D is technically correct in context as all these terms are used interchangeably in electrical engineering literature to describe this phenomenon.

Answer: B is correct — $I \sin(\Phi)$ is defined as the reactive component of the total current because it is in quadrature with the supply voltage.

Exam Tip: Always remember that in engineering terminology, 'Wattless', 'Reactive', and 'Quadrature' are synonyms for the same current component; if you see this in an exam, evaluate if 'All the above' is a better fit than a single specific term.

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