Phasor Analysis Tool

A phasor is a complex number representing a sinusoidal function (e.g., an AC voltage or current) whose amplitude ($A$), angular frequency ($\omega$), and initial phase ($\phi$) are time-invariant. Phasors simplify the analysis of circuits with sinusoidal signals by converting differential equations into algebraic ones.

A sinusoidal waveform $v(t) = V_m \cos(\omega t + \phi)$ can be represented by the phasor $\mathbf{V} = V_m \angle \phi$.

• $V_m$ is the peak amplitude of the sinusoid.
• $\phi$ is the phase angle of the sinusoid in degrees or radians.
• The frequency $\omega$ is usually implicit and common to all phasors in a given problem.

Phasors can be represented in:

• Polar Form: $V_m \angle \phi$ (Magnitude and Angle)
• Rectangular/Cartesian Form: $a + jb$, where $a = V_m \cos\phi$ and $b = V_m \sin\phi$. (Note: Electrical engineers often use $j$ for the imaginary unit to avoid confusion with current $i$). We will use $i$ for consistency with general mathematics.

Graphically, a phasor is represented as a vector in the complex plane, originating from the origin, with length $V_m$ and making an angle $\phi$ with the positive real axis.