The time axis of an ac phasor represents?

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Examoogle · Accepted Answer

Phase angle

Explanation: In phasor notation, the horizontal axis of the complex plane represents the phase angle $	heta$ (relative to a reference vector at $t=0$), while the vertical axis represents the imaginary component. Phasors rotate at a constant angular velocity $\omega$, effectively transforming the time-domain sinusoidal waveform into a stationary vector representation where the rotation angle corresponds to $\omega t$.

Working Principle: A sinusoidal function $v(t) = V_m \sin(\omega t + \phi)$ is represented as a complex number $V = V_m \angle \phi$. The phasor itself is a snapshot of this rotating vector at time $t=0$. Because the vector rotates at constant speed $\omega$, the position of the phasor in the complex plane effectively maps the 'time' progress into an angular position $	heta = \omega t + \phi$.

Key Formulas: $v(t) = V_m \sin(\omega t + \phi)$ — Time domain representation; $\vec{V} = V_m e^{j\phi}$ — Phasor domain representation; $	heta = \omega t$ — Angular conversion of time

Key Points: Phasors are time-invariant representations of sinusoidal quantities.; The projection of a phasor onto the real or imaginary axis gives the instantaneous value.; The phase angle $\phi$ is measured relative to the reference axis (usually the real axis).; Phasors eliminate the need for solving differential equations in AC circuits.

Advantages: Converts differential equations to algebraic equations.; Simplifies analysis of steady-state AC circuits.

Disadvantages: Applicable only to linear circuits with sinusoidal inputs.; Does not represent transient state behavior.

Applications: Power system load flow analysis.; AC circuit steady-state analysis.; Signal processing and communication theory.

Additional Info: In phasor diagrams, the angle $	heta$ represents the phase offset of the waveform relative to the origin.. Time is explicitly removed from the phasor domain because steady-state sinusoidal response in linear circuits maintains the same frequency $\omega$.

Answer: B is correct — The time axis of a phasor diagram is replaced by the angular position $	heta$, representing the phase displacement of the quantity.

Exam Tip: Remember that in a phasor diagram, 'rotating' the phasor counter-clockwise signifies the passage of time; hence, angular displacement is the direct substitute for time.

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