The length of the phasor represents?

Question

Examoogle · Accepted Answer

Magnitude of the quantity

Explanation: A phasor is a complex number representing a sinusoidal function, where its length (magnitude) corresponds to the peak or RMS value of the physical quantity (voltage or current), and its angle represents the phase shift.

Working Principle: In steady-state AC analysis, a sinusoidal signal $A(t) = A_m \cos(\omega t + \phi)$ is represented as a complex phasor $A = A_m \angle \phi$. The rotating vector's projection on the real axis at $t=0$ gives the instantaneous value, where the vector's length represents the amplitude $A_m$ and the angle $\phi$ with the positive real axis represents the phase angle relative to the reference signal.

Key Formulas: $A = A_m e^{j\phi} = A_m(\cos \phi + j \sin \phi)$ — Complex representation of a phasor; $V_{rms} = \frac{V_m}{\sqrt{2}}$ — Relationship between peak magnitude and RMS value

Key Points: A phasor is a snapshot of a rotating vector at $t=0$.; Phasors are applicable only to linear time-invariant systems with sinusoidal inputs.; The length (magnitude) is constant for a given phasor representation.; The phase angle is measured counter-clockwise from the positive real axis.

Advantages: Converts differential equations into simple algebraic equations; Simplifies addition and subtraction of sinusoidal signals

Disadvantages: Only applicable to sinusoidal steady-state analysis; Cannot be used for non-linear circuits or transient responses

Applications: AC Power Systems; Control Systems stability analysis; Signal Processing

Additional Info: The phase of the quantity is represented by the angle the phasor makes with the positive real axis.. Option B is incorrect because the phasor's orientation (angle), not its length, indicates the phase/direction of the quantity.. Phasors are essentially complex numbers in polar or rectangular form.

Answer: A is correct — The length (magnitude) of a phasor represents the maximum (peak) or RMS amplitude of the sinusoidal quantity being represented.

Exam Tip: Remember that phasors represent magnitude and phase, whereas vectors (in physics) represent magnitude and direction in space; do not confuse them.

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