What a Phasor Represents
A phasor represents one sinusoidal quantity at one frequency. Its magnitude may be RMS or peak, and its angle is measured relative to a chosen reference.
x(t) = X cos(ωt + θ) → X∠θ
Every phasor in one calculation must use the same frequency and magnitude convention.
Rectangular and Polar Form
Rectangular form separates real and imaginary components. Polar form emphasizes magnitude and angle.
a + jb = M∠θ
M = √(a² + b²) θ = atan2(b, a)
Add and subtract in rectangular form. Multiply magnitudes and add angles; divide magnitudes and subtract angles.
AC Circuit Meaning
Resistance lies on the real axis. Ideal inductive reactance is positive imaginary impedance, while ideal capacitive reactance is negative imaginary impedance. The resulting impedance angle affects the phase between voltage and current.
For example, 120∠0° V across 10∠30° Ω gives 12∠-30° A.
Common Mistakes
- Mixing degrees and radians.
- Mixing RMS and peak magnitudes.
- Adding polar values directly instead of converting to rectangular form.
- Using phasors for transients or signals at different frequencies.