Phasor Addition (V_R, V_L, V_C)

A phasor is a rotating vector representing a sinusoidal quantity — its length is the amplitude, its angle is the phase.

All phasors in a circuit rotate at the SAME angular frequency ω. Relative phase angles between them stay constant.

By convention, we view the phasors in a rotating frame so the current is along the +x axis. Voltage phasors are drawn relative to it.

For R: V_R is in phase with I (along +x).

For L: V_L leads I by +90° (along +y).

For C: V_C lags I by −90° (along −y).

Total source voltage = vector sum of V_R, V_L, V_C. For series LCR: V = √(V_R² + (V_L − V_C)²).

Adding phasors graphically gives both the magnitude (Z·I) and phase (φ = tan⁻¹((X_L−X_C)/R)).