Library / Electrical / ELE-26
Electrical
Series RLC impedance
Total opposition to alternating current in a series circuit.
- Ref
- ELE-26
- Rev
- v1
- Field
- Electrical
- Result
- Z [Ω]
R is the resistance, XL = ωL the inductive reactance and XC = 1/(ωC) the capacitive reactance, all in ohms at the operating frequency. Because the two reactances are 180° apart in phase, they subtract. Z is the size of the total opposition; the current is I = V/Z.
Total opposition to alternating current in a series circuit. The reactances partly cancel; at resonance they cancel fully and only R is left.
Calculator
- Net reactance XL − XC40 Ω
- Phase angle of the voltage ahead of the current53.13 °
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The defaults give a 30-40-50 triangle: R = 30 Ω, net reactance 40 Ω, Z = 50 Ω. The voltage leads the current by 53°, so the circuit looks inductive.
- When XL = XC the reactance cancels completely, Z falls to its minimum R, and the current peaks: that is resonance.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Ω) | Local step | Change in result |
|---|---|---|---|---|---|---|
| R Resistance | 0.1 to 1,000 Ω | 40 | 1,001 | 960.8 | +10% | +3.71 % |
| XL Inductive reactance | 0 to 1,000 Ω | 30.18 | 970.5 | 940.3 | +10% | +11.5 % |
| XC Capacitive reactance | 0 to 1,000 Ω | 30.18 | 930.5 | 900.3 | +10% | −4.73 % |
Sweep of Capacitive reactance
| Capacitive reactance (Ω) | Impedance (Ω) |
|---|---|
| 0 | 76.16 |
| 125 | 62.65 |
| 250 | 182.5 |
| 375 | 306.5 |
| 500 | 431 |
| 625 | 555.8 |
| 750 | 680.7 |
| 875 | 805.6 |
| 1,000 | 930.5 |
Sweep one variable
Variables and how each one contributes
Impedance
What the equation gives you. Everything else feeds it.
Resistance
The resistance of the circuit. Matters more when the net reactance is small. At the default a 10 % rise in R (3 Ω) raises Z by about 3.7 %; at resonance Z equals R.
Inductive reactance
The inductive reactance, which rises with frequency. Raises Z when XL is above XC. A 10 % rise in XL (7 Ω) raises Z by about 11.5 %, the strongest lever here, because it widens the net reactance.
Capacitive reactance
The capacitive reactance, which falls with frequency. Lowers Z while XC is below XL, because it cancels part of the inductive reactance: a 10 % rise (3 Ω) lowers Z by about 4.7 %. Past XL it raises Z again.
Worked example with the values above
- Net reactance: XL − XC = 70 − 30 = 40 Ω.
- Squares: R² + (XL − XC)² = 900 + 1,600 = 2,500.
- Z = √2,500 = 50 Ω.
Assumptions and limits
- A single frequency, steady-state sine wave, with linear components.
- R, L and C connected in series, with ideal inductor and capacitor.
Common mistakes
- Adding XL and XC instead of subtracting them.
- Adding R and the reactance directly instead of in quadrature.
Statistics and uncertainty
Z is the square root of a sum of squares, so the larger of R and the net reactance dominates. Near resonance the small net reactance is a difference of two large numbers and is very sensitive: a 1 % mismatch between two 1000 Ω reactances leaves 10 Ω of net reactance, which can exceed R.
Where it is used
- Finding the current drawn by a tuned circuit or filter.
- Choosing a capacitor to cancel an inductive load.
Maths you need
- Reactance: XL = ωL, XC = 1/ωC
- Pythagoras: combining at right angles