LC Series Impedance Calculator

Calculate the impedance of a series LC circuit. Enter inductance, capacitance, and frequency to get the inductive and capacitive reactances, the magnitude of the combined impedance, and the resonant frequency.

Input

Calculate the impedance of an AC circuit with an inductor L and a capacitor C in series. Enter L, C, and the frequency f.

Inductance L

Inductance of the coil in henrys

Capacitance C

Capacitance of the capacitor in farads

Frequency f

Frequency of the AC signal in hertz

Result

Total impedance |Z|

96.32309Ω

Capacitive (phase -90 degrees)

Inductive reactance X_L

62.831853 Ω

Capacitive reactance X_C

159.154943 Ω

Resonant frequency f0

1,591.549431 Hz

X_L = omega times L, X_C = 1 divided by (omega times C), |Z| = |X_L minus X_C|, and f0 = 1 divided by (2 times pi times the square root of L times C), with omega = 2 times pi times f.

How it works

A series LC circuit connects an inductor L and a capacitor C in line, and because it has no resistance the total impedance equals the magnitude of the difference of the two reactances.
The angular frequency omega equals 2 times pi times the frequency f. The inductive reactance is X_L = omega times L, and the capacitive reactance is X_C = 1 divided by (omega times C).
The magnitude of the impedance is the absolute value of the difference of X_L and X_C, written |Z| = |X_L minus X_C|.
When X_L is greater than X_C the circuit is inductive with a phase of +90 degrees; when smaller it is capacitive with minus 90 degrees.
When X_L equals X_C the circuit is at series resonance, where the impedance is 0 ohm and the phase is 0 degrees.
The resonant frequency f0 equals 1 divided by (2 times pi times the square root of L times C), and at this frequency the current is at its maximum.
L is in henrys (H), C in farads (F), f in hertz (Hz), and reactance and impedance in ohms (Ω).

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