Phasor Representation of Alternating Quantity

Understanding how to represent alternating quantities like voltage and current is crucial in electrical engineering. Alternating quantities vary sinusoidally with time. To simplify analysis, especially in circuits with components like resistors, inductors, and capacitors, we use phasor representation.

A phasor is essentially a rotating vector that represents a sinusoidally varying quantity at a specific frequency. Here's how it works:

• It is represented graphically by a straight line with an arrow at one end.
• The length of this line (the magnitude of the vector) represents the maximum value (amplitude) or the RMS value of the alternating quantity.
• This straight line is imagined to rotate counterclockwise about the origin (or a fixed point) with an angular velocity equal to the angular frequency ($\omega$) of the alternating quantity.
• The angle that the phasor makes with the positive horizontal axis (often representing the reference phase, like time $t=0$) represents the phase angle of the alternating quantity.
• The projection of this rotating vector onto the vertical axis gives the instantaneous value of the alternating quantity.

Therefore, the graphical representation of a phasor is fundamentally a straight line with an arrow indicating its direction and magnitude in the complex plane, or a plane representing phase relative to a reference.

Let's consider the given options:

• zigzag form: A zigzag form does not represent a single alternating quantity in its phasor form.
• a straight line with an arrow: This correctly describes a vector, which is the basis of a phasor representation. The straight line has a specific length (magnitude) and the arrow indicates direction (phase).
• hyperbolic linear form: Hyperbolic forms are not used for representing sinusoidal alternating quantities graphically as phasors.
• a line defining variable points is some distance: While the instantaneous value varies, the phasor itself is a fixed representation (magnitude and relative phase) for a specific sinusoidal quantity at a given frequency, usually depicted as rotating. The representation itself is not a line defining variable points in this context; it's a static depiction of the rotating vector at a particular instant or its characteristics (magnitude and phase).

Based on the definition and graphical representation of a phasor, the correct description is a straight line with an arrow.