RLC Impedance – Phasor Sum
A resistor, an inductor and a capacitor in series. Together they oppose the AC current with a total impedance Z. The phasor diagram rotates to show the alternating signal.
Z = √(R² + (X L − X C )²) φ = atan((X L − X C ) / R)
Meet the three parts
Resistor (R)
Electrons bump through the zigzag and turn energy into heat. Voltage and current rise and fall together, so they are in phase. R stays the same at every frequency.
X R = R φ = 0°Inductor (L)
The coil builds a magnetic field and resists any change in current. Voltage peaks first and current follows 90° later. Faster signals meet more opposition.
X L = 2πfL i lags vCapacitor (C)
Current flows only while the plates charge or discharge, so current peaks before voltage: it leads by 90°. Faster signals meet less opposition.
X C = 1 / (2πfC) i leads vPutting them together
In a series circuit the same current flows through all three parts. So the three oppositions are drawn as phasors: R along the current, X L 90° ahead, X C 90° behind. Added tip to tail, X L and X C partly cancel, and the result is Z. Try it below.
Live demo
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