Series Rlc Impedance
Calculator
Results
- Impedance (Ω)
- 303.822553
- Inductive reactance (Ω)
- 31.415926
- Capacitive reactance (Ω)
- 318.309886
- Phase angle (degrees)
- -70.783445
Electrical results
| Impedance (Ω) | 303.822553 |
| Inductive reactance (Ω) | 31.415926 |
| Capacitive reactance (Ω) | 318.309886 |
| Phase angle (degrees) | -70.783445 |
formula-map diagram
- Impedance (Ω)
- 303.822553
- Inductive reactance (Ω)
- 31.415926
- Capacitive reactance (Ω)
- 318.309886
- Phase angle (degrees)
- -70.783445
Electrical relationship
Formula
Z = √(R² + (XL − Xc)²)= 303.82255361057
Note
This is a simplified model: it applies the textbook relationship to the numbers you entered and assumes ideal components, steady-state sinusoidal conditions, balanced loads and copper resistivity of 0.0172 Ω·mm²/m at 20 °C. It ignores component tolerances, temperature drift, skin effect, harmonics, inrush, transformer and battery losses, and it is not a substitute for the wiring code that applies where you are. Have any installation sized and verified by a licensed electrician or engineer.
More in Electrical engineering
See all →Frequently asked questions
How is the total impedance of a series RLC circuit calculated?+
Z = sqrt(R^2 + (XL - XC)^2), combining resistance with the net reactance. Because XL and XC point in opposite directions on the phasor diagram, they partially cancel before being combined with R.
Why do XL and XC subtract instead of add in the formula?+
Inductive and capacitive reactances create voltage drops that are 180 degrees out of phase with each other, so their effects oppose rather than reinforce. This subtraction is what allows the circuit to reach a minimum impedance at resonance.
What does it mean when XL equals XC?+
The reactive terms cancel completely, leaving Z = R — this is the resonance condition, where the series RLC circuit offers its lowest possible impedance and allows maximum current for a given voltage.
Is the impedance the same as adding R, L, and C reactances directly?+
No, you can't just add ohms of resistance and reactance arithmetically because they're 90 degrees out of phase with each other; that's why the formula uses the Pythagorean-style square root of sums of squares rather than plain addition.
How does impedance affect current in the circuit?+
Total current is found the same way as with pure resistance, I = V / Z, but the current will be phase-shifted relative to the voltage unless the circuit is exactly at resonance, where the phase shift is zero.