\[Z=\sqrt{R^2+\left(X_L-X_C\right)^2}\]
Variables
Zimpedance (ohm)
Rresistance (ohm)
Xlinductive reactance (ohm)
Xccapacitive reactance (ohm)
Description
What is this formula?
This formula calculates the total impedance of a series RLC circuit from its resistance and reactances.
When to use it
Use it when analyzing alternating current circuits containing resistors, inductors, and capacitors connected in series.
Example
Data:
R = 50 ohm
Xl = 120 ohm
Xc = 80 ohm
Formula:
Z = sqrt(R^2+(Xl-Xc)^2)
Substitution:
Z = sqrt(50^2+(120-80)^2)
Result:
Z = 64.0 ohm
Applications
AC circuit analysis, resonance studies, filter design, power electronics, impedance matching, and electrical engineering.