Phasor Addition (V_R, V_L, V_C)
Vector sum: V = √(V_R² + (V_L − V_C)²). Tune each and see V_net.
Key Notes
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)).
Formulas
Phasor representation
Phasor encodes amplitude and initial phase.
Phasor addition (rms)
Pythagorean, because V_L and V_C are antiparallel.
Phase angle
Sign indicates lead/lag of V w.r.t. I.
Power factor (from phasor)
Adjacent/hypotenuse on the voltage phasor triangle.
Important Points
Phasors are a CALCULATION TRICK — they exploit the fact that sums and differences of sinusoids of the same ω are still sinusoids of that ω.
All phasors must reference the SAME ω. You can't add phasors of different frequencies.
Phasor diagrams use the current direction as reference because current is the same throughout a series circuit.
Phasor lengths represent RMS or peak — be consistent. Don't mix.
V_L and V_C are along the SAME line but OPPOSITE directions — one of them gets subtracted in magnitude.
Phasor analysis is the bridge to complex impedance (Z = R + jX) and the basis of all AC circuit theory.
Phasor Addition (V_R, V_L, V_C) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.