impedance

Once frequency matters, plain resistance is no longer enough, because reactive parts both oppose current and shift its timing. Impedance is the full story: the total opposition to AC, capturing both how much the current is reduced and how much it is phase-shifted. It is the honest replacement for resistance in the AC world.

Impedance Z combines resistance R and reactance X. Because reactance acts 90 degrees out of phase, you cannot just add them; you combine them at right angles. The magnitude is the square root of (R^2 + X^2), and the phase angle is arctan(X/R). Example: 30 ohms of resistance in series with 40 ohms of reactance gives an impedance magnitude of the square root of (900 + 1600) = 50 ohms, at a phase angle of about 53 degrees. Ohm's law still works in this richer form: V = I times Z, treated as complex quantities.

Impedance governs filters, matching, loading between stages, and how much a signal source can drive a load at a given frequency. Caveat: impedance is a single number only at one frequency. It changes as frequency changes, so the impedance of a capacitor or a speaker is really a curve, not one figure. Engineers often picture it as a complex number or a phasor to keep magnitude and phase together.