Formula
Inductive reactance is 2πfL. Capacitive reactance is 1 / (2πfC). In series, the imaginary part is XL − XC, the magnitude is the hypotenuse with R, and the phase is the arctangent of that imaginary part over R. In parallel, conductance is 1/R and susceptance is ωC − 1/(ωL). Impedance magnitude is 1 over the admittance magnitude. The phase of the impedance is the opposite of the phase of the admittance.
XL = 2π f L
XC = 1 / (2π f C)
|Zseries| = √(R² + (XL − XC)²)
A zero inductance or capacitance is left out of that term, which is how the reactance-only mode can show one part. Resonance, where XL equals XC, is also on the filter calculator. A real load on 50 Ω coax is the SWR calculator.
Worked examples
1 kHz, 10 mH, 1 µF. XL is 62.832 Ω. XC is 159.155 Ω.
Series with 100 Ω. Magnitude 138.85 Ω, phase −43.93°.
The same three parts in parallel. Magnitude 72.02 Ω, phase +43.93°.
Reference
Phase is in degrees, lagging negative. These are ideal parts at one frequency.
Questions
What is the reactance of 10 mH at 1 kHz?
62.83 Ω, from 2πfL. A 1 µF capacitor at the same frequency is 159.15 Ω.
What is the series impedance with 100 Ω?
The net reactance is 62.83 − 159.15 = −96.32 Ω. Magnitude is 138.85 Ω. Phase is −43.93°.
How is the parallel case different?
The resistor, inductor, and capacitor share the voltage. Susceptance is ωC − 1/(ωL). Impedance magnitude is 1 over the admittance magnitude. With the same parts the parallel magnitude is 72.02 Ω at +43.93°.
Sources
- XL = 2πfL and XC = 1/(2πfC).
- Series Z = R + j(XL − XC). Parallel Y = 1/R + j(ωC − 1/(ωL)).