What Happens to Circuit Impedance at LC Resonance?

In electronics, LC resonance occurs at a specific frequency where a circuit's inductive reactance and capacitive reactance become equal in magnitude and cancel each other out. This article provides a clear breakdown of how this cancellation directly affects circuit impedance, explaining why impedance drops to an absolute minimum in series LC circuits and rises to an absolute maximum in parallel LC circuits, leaving the circuit to behave purely resistively.

The Cancelation of Reactances

Impedance (\(Z\)) is the total opposition a circuit presents to alternating current (AC). It is made up of two parts: real resistance (\(R\)) and reactance (\(X\)). Reactance comes in two forms:

  • Inductive Reactance (\(X_L\)): Increases as the AC frequency increases.
  • Capacitive Reactance (\(X_C\)): Decreases as the AC frequency increases.

Because these two reactances behave in opposite ways and are 180 degrees out of phase with one another, there is a specific frequency—known as the resonant frequency—where \(X_L\) and \(X_C\) are identical in value. At this exact point, they completely cancel each other out. However, what happens to the total impedance of the circuit depends entirely on whether the inductor and capacitor are wired in series or in parallel.

Impedance in a Series LC Circuit

In a series LC circuit, the inductor and capacitor are connected end-to-end along the same path. The formula for total impedance in a series circuit is:

\(Z = \sqrt{R^2 + (X_L - X_C)^2}\)

At resonance, because \(X_L\) equals \(X_C\), subtracting one from the other results in zero total reactance.

  • Ideal Circuit: If there were zero resistance in the wires, the total impedance would drop to zero (\(0\ \Omega\)). The circuit would act like a complete short circuit at the resonant frequency.
  • Real-World Circuit: Because all physical components and wires have some inherent resistance, the impedance simply drops to its minimum possible value, which is equal to the circuit's pure DC resistance (\(Z = R\)).

With impedance at its lowest point, the circuit allows the maximum possible amount of current to flow at the resonant frequency.

Impedance in a Parallel LC Circuit

In a parallel LC circuit (often called a "tank circuit"), the inductor and capacitor are connected in parallel branches. The behavior of impedance at resonance here is the exact opposite of a series circuit.

At the resonant frequency, energy continuously bounces back and forth between the magnetic field of the inductor and the electric field of the capacitor. Because the currents in the two branches are equal and opposite, they cancel each other out from the perspective of the main power source.

  • Ideal Circuit: With no energy lost to resistance, no current needs to enter or leave the parallel loop from the main source to keep the oscillation going. Since zero current is drawn from the source, the impedance of the parallel loop appears to be infinite (\(\infty\ \Omega\)). It acts like an open circuit.
  • Real-World Circuit: Small resistances within the inductor's coils and the capacitor's leads cause some energy loss. Therefore, the circuit draws a tiny amount of current from the source to replenish this lost energy. As a result, the impedance does not reach infinity, but instead reaches its maximum possible value.

With impedance at its highest point, a parallel LC circuit blocks current at the resonant frequency while allowing other frequencies to pass.

Phase Angle and Pure Resistance

Regardless of whether the circuit is in series or parallel, the cancellation of inductive and capacitive reactances alters the phase angle of the circuit. Outside of resonance, the voltage and current are out of phase. At resonance, because the reactive components are gone, the circuit becomes purely resistive. This causes the voltage and current to align, putting them completely in phase with a phase angle of zero degrees.