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Series RL or RC Impedance

Z=R2+X2Z = \sqrt{R^{2} + X^{2}}

Worked example: 40 Ω R with 30 Ω X → 50 Ω — press Try an example to run it live, then adjust anything.

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Series RL or RC Impedance explained

RXZ

A resistor's voltage is in phase with its current, a reactance's is a quarter cycle away, so their oppositions add as the legs of a right triangle: 40 Ω of resistance with 30 Ω of reactance gives 50 Ω, not 70 Ω. This is the everyday impedance calculation — the winding resistance and inductance of a relay coil, a contactor, a transformer primary, a loudspeaker crossover leg.

The same triangle hands you the phase angle, φ = arctan(X/R), and hence the power factor cos φ = R/Z. That is worth remembering when you meet an inductive load with no nameplate: measure the DC resistance, measure the AC current at a known voltage to get Z, and the power factor falls out of the ratio. Rough numbers are enough to tell a mostly resistive load from a mostly reactive one.

Series RL or RC Impedance formula

Z=R2+X2Z = \sqrt{R^{2} + X^{2}}
Where
  • ZZ= Impedance magnitude (Ω)
  • RR= Resistance (Ω)
  • XX= Reactance (Ω)

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