A resistor opposes current by the same number of ohms whether the current is steady or racing. Coils and capacitors do not. Their opposition — called reactance, and measured in ohms all the same — depends entirely on the frequency, and the two of them move in opposite directions.

$X_L = 2\pi f L$, read aloud X-L equals two pi f L. $X_L$ is the inductive reactance in ohms, $f$ is the supply frequency in hertz, and $L$ is the inductance in henries. Every factor is on top, so everything makes the opposition bigger: a coil fights change, and the faster you ask it to change, the harder it fights. At DC, where $f = 0$, a perfect coil is a plain piece of wire.

$X_C = \dfrac{1}{2\pi f C}$ — X-C equals one over two pi f C. $X_C$ is the capacitive reactance in ohms, with the same $f$ in hertz and $C$ the capacitance in farads. Everything is downstairs, so everything makes the opposition smaller. At DC the reactance is infinite — a capacitor blocks steady current outright — and at high frequency it approaches a short circuit, which is exactly the job description of a bypass capacitor.

The 2π is not decoration and it is not optional: it converts cycles per second into radians per second, because the underlying rate of change is angular. Dropping it is the single most common slip in this chapter, and it is always wrong by the same factor of 6.28. If a reactance looks six times off, that is the first place to look.