Impedance (RLC)

In a series RLC circuit, resistance and reactance do not simply add because they act differently: resistance is in phase with the current, while inductive and capacitive reactances act in opposite reactive directions. The quantity \(X_L - X_C\) gives the net reactive effect, and combining that at right angles with \(R\) using the Pythagorean theorem gives the magnitude of the total AC opposition, called impedance. This is why impedance can be larger or smaller than resistance alone, and it becomes equal to \(R\) at resonance when \(X_L = X_C\).

Use this formula for series AC circuits containing resistors, inductors, and capacitors when you need the total opposition to current, especially to find current from an applied AC voltage. It is also essential for resonance problems, filter analysis, and determining how a circuit's response changes with frequency.

• Adding \(X_L\) and \(X_C\) instead of subtracting them to get the net reactance
• Using the formula for parallel circuits, where impedance must be found differently
• Forgetting that the result is always a magnitude, so \(Z\) should be reported as a positive value