The resultant of two alternating sinusoidal voltages or currents can be found using

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Parallelogram law

Explanation: The resultant of two sinusoidal voltages or currents of the same frequency is determined by treating them as phasors, which are rotating vectors. The Parallelogram law of vector addition is the standard geometric method used to find the vector sum (resultant) of these two phasors.

Working Principle: When two alternating quantities with the same frequency are represented as vectors (phasors) starting from a common origin, their instantaneous sum is a third vector defined by the diagonal of a parallelogram constructed using the two original vectors as adjacent sides. The magnitude and phase angle of the resultant depend on both the individual magnitudes and the phase difference between them.

Key Formulas: $R = \sqrt{A^2 + B^2 + 2AB \cos(\phi)}$ — Resultant magnitude of two phasors A and B with phase angle \phi; $\alpha = 	an^{-1}\left(\frac{B \sin(\phi)}{A + B \cos(\phi)}ight)$ — Phase angle of the resultant

Key Points: Phasor addition is only applicable to sinusoidal quantities of the same frequency.; The resultant is a phasor representing the sum of the two individual quantities.; Both magnitude and phase must be considered, making vector addition necessary instead of scalar addition.

Advantages: Simplifies complex time-domain differential equations into algebraic operations; Allows clear visualization of phase relationships between voltage and current

Disadvantages: Inapplicable to non-sinusoidal waveforms; Requires constant frequency for all phasors in the summation

Applications: Calculating branch currents in AC series/parallel circuits; Analyzing three-phase power systems

Additional Info: The Triangle law of vector addition is a special case derived from the Parallelogram law; however, in standard AC circuit analysis, the Parallelogram law is the convention used for resultant phasor calculation.. Option A is a subset of the geometric construction process, but Option B is the formal term for the vector addition method.

Answer: B is correct — The Parallelogram law of vector addition is the mathematically correct method for finding the resultant of two sinusoidal quantities represented as phasors.

Exam Tip: Always remember that phasors are rotating vectors; you can only add them directly if they share the same frequency, otherwise, you must use instantaneous time-domain summation.

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