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Series RLC Impedance

Z=R2+(XL−XC)2Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}

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Reactances are 90° out of phase with resistance and 180° out of phase with each other, so they subtract first and then join R by Pythagoras. With R = 30 Ω, XL = 80 Ω and XC = 40 Ω, the net reactance is 40 Ω and Z = √(30² + 40²) = 50 Ω. Note that reactances can each be far larger than the total impedance — at resonance they cancel exactly and Z collapses to R alone, which is how a tuned circuit picks one station out of the air.

Because the square root discards sign, solving for a reactance has two answers; this brain returns the inductive-dominant branch (XL above XC), so subtract the root instead if you know the circuit is capacitive. The practical warning: never add reactances arithmetically to resistance. A 300 Ω coil in series with 400 Ω of resistance is 500 Ω, not 700 Ω, and a meter that reads otherwise is measuring DC.

Series RLC Impedance
Z=R2+(XL−XC)2Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}
Where
  • ZZ= Impedance magnitude
  • RR= Resistance
  • XLX_{L}= Inductive reactance
  • XCX_{C}= Capacitive reactance
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