AC foundations
Series RLC impedance
- where
- impedance magnitude (Ω)
- resistance (Ω)
- inductive reactance magnitude (Ω)
- capacitive reactance magnitude (Ω)
Explain this equation
Works out the total opposition to AC in a series circuit with resistance, inductance and capacitance. Used to find current in AC circuits that are not purely resistive.
|Z| is the size of the impedance in ohms. R is resistance. Xₗ and X꜀ are the inductive and capacitive reactances. Xₗ − X꜀ is the net reactance, because the two pull in opposite directions.
Resistance and reactance act 90° apart, so they combine like the sides of a right-angled triangle. The impedance is the hypotenuse, which is where the square root comes from.
Sense check: 3 Ω with 5 Ω inductive and 1 Ω capacitive gives √(9 + 16) = 5 Ω. |Z| can never be less than R.
Watch out: do not simply add R and X. All values must be at the same frequency.
Subtract capacitive reactance from inductive reactance to find the net reactive component. Resistance and net reactance are perpendicular components, so use Pythagoras.
If X꜀ is greater, the net reactance is negative, but impedance magnitude is still positive.
Enter your values to see the result.
Common mistake
Adding R and reactance magnitudes arithmetically.
Limits
Series RLC at one sinusoidal frequency.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.