RLC Impedance Calculator: Series Circuit Z, Resonance, Q Factor

Impedance (Z) is the total opposition to alternating current in a circuit, combining resistance (R), inductive reactance (XL), and capacitive reactance (XC). It is measured in ohms (Ω) and is a complex quantity with both magnitude and phase angle. In a series RLC circuit, Z = sqrt(R² + (XL - XC)²). Unlike resistance, impedance changes with frequency because XL and XC are frequency-dependent. Ohm's law for AC circuits uses impedance: I = V / Z.

The resonant frequency (f0) is the frequency at which inductive reactance (XL) exactly equals capacitive reactance (XC), so they cancel each other out. The formula is f0 = 1 / (2 * π * sqrt(L * C)), where L is inductance in henries and C is capacitance in farads. At resonance, the impedance of a series RLC circuit is at its minimum (equal to R alone), and the current is at its maximum for a given applied voltage.

The Q factor (quality factor) is a dimensionless measure of how selective or narrow-band a resonant circuit is. For a series RLC circuit, Q = (1/R) * sqrt(L/C). A high Q means the circuit resonates sharply at f0 with little energy loss, while a low Q indicates a broad, lossy resonance. Q also equals the ratio of the resonant frequency to the 3 dB bandwidth: Q = f0 / BW. High-Q circuits are used in radio tuners, filters, and oscillators.

At resonance in a series RLC circuit, XL = XC, so they cancel and the net reactive impedance is zero. The total impedance reduces to Z = R (purely resistive). This is the minimum impedance point, meaning the circuit draws maximum current for the applied voltage. The voltage across the inductor and capacitor can be much larger than the source voltage (by a factor of Q), which is why resonant circuits can produce voltage magnification and must be handled carefully in high-Q designs.

The phase angle (θ) in a series RLC circuit is the angle between the total voltage and the current, calculated as θ = atan2(XL - XC, R). When XL is greater than XC (above resonance), θ is positive and the circuit is inductive: voltage leads current. When XC is greater than XL (below resonance), θ is negative and the circuit is capacitive: current leads voltage. At resonance (XL = XC), θ is zero and the circuit is purely resistive.