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.
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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 of the coil in henrys
Capacitance of the capacitor in farads
Frequency of the AC signal in hertz
Result
Total impedance |Z|
96.32309ฮฉ
Capacitive (phase -90 degrees)
Inductive reactance X_L
62.831853 ฮฉ
Capacitive reactance X_C
159.154943 ฮฉ
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 (ฮฉ).
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