RLC Impedance Calculator

Impedance, denoted by the symbol Z and measured in ohms, combines resistance (R), inductive reactance (X_L), and capacitive reactance (X_C). In a series RLC circuit, angular frequency is calculated as ω = 2πf. Inductive and capacitive reactances are defined as X_L = ωL and X_C = 1 / (ωC) respectively. The total series impedance is found using the formula Z = √[R² + (X_L - X_C)²]. For parallel circuits, the calculation uses admittances, combining the inverse squares of resistance and reactances to determine the overall network impedance.

Let us calculate the series impedance of an RLC circuit operating at a frequency of 1,000 Hz. Suppose our circuit contains a resistor of 100 ohms (R = 100 Ω), an inductor of 50 millihenries (L = 0.05 H), and a capacitor of 1 microfarad (C = 1 × 10^-6 F). First, find the angular frequency: ω = 2 × π × 1000 ≈ 6,283.18 rad/s. Next, compute inductive reactance: X_L = 6,283.18 × 0.05 ≈ 314.16 Ω. Then, calculate capacitive reactance: X_C = 1 / (6,283.18 × 0.000001) ≈ 159.15 Ω. Finally, substitute these values into the impedance formula: Z = √[100² + (314.16 - 159.15)²] = √[10,000 + 24,028.02] = √34,028.02 ≈ 184.47 Ω.

When working with AC circuit calculations, always ensure your units are consistent—convert microfarads to farads and millihenries to henries before plugging numbers into formulas. Pay close attention to whether your circuit topology is series or parallel, as the mathematical formulas for combining components differ significantly. Finally, keep in mind that at resonant frequency, inductive and capacitive reactances cancel each other out in series circuits, leaving impedance solely equal to the resistance value.