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Formula Impedance (RLC series circuit) Inductance    Capacitance    Angular frequency    Resistance

Formula
Formula: Impedance (RLC series circuit)

Impedance

Unit
Impedance is the magnitude of the complex resistance \( Z \). This formula gives the total impedance of a resistor-coil-capacitor series circuit (RLC series circuit). To obtain this formula, the Pythagorean theorem was applied to a phasor diagram on which the three quantities are plotted:
  • Ohmic impedance: \(Z_{\text R } ~=~ R \).
  • Inductive impedance: \(Z_{\text L } ~=~ \text{i} \, \omega \, L \).
  • Capacitive impedance: \(Z_{\text C } ~=~ -\text{i}\frac{1}{\omega \, C} \).

Inductance

Unit
The inductance of the coil connected to the RLC circuit.

Capacitance

Unit
Capacitance of the capacitor connected to the RLC circuit.

Angular frequency

Unit
The angular frequency \( \omega = 2\pi \, f \) indicates the frequency \(f\) at which the LRC circuit oscillates. The frequency \(f\) is specified, for example, by the frequency of the applied AC voltage.

Resistance

Unit
Ohmic resistance of a resistor connected to the RLC series circuit.