How capacitive reactance shapes RC filters
Why a capacitor's frequency-dependent reactance turns a resistor-capacitor pair into a low-pass or high-pass filter, and how to find the cutoff.
Reactance is frequency dependent
Unlike a resistor, whose ohms stay put across frequency, a capacitor's reactance changes with the signal. The formula Xc = 1 / (2 pi f C) means low frequencies see a large reactance and high frequencies see a small one. A 1 microfarad capacitor presents about 159 ohms at 1 kHz but only about 16 ohms at 10 kHz. That single fact, reactance sliding as frequency moves, is what lets a plain resistor-capacitor pair sort signals by frequency instead of treating them all alike.
Low-pass and high-pass from the same parts
Put a resistor in series and take the output across the capacitor, and you have a low-pass filter: at low frequencies the capacitor's high reactance keeps most of the voltage, while at high frequencies its low reactance shorts the signal to ground and the output drops. Swap the output to the resistor instead, and the same two parts become a high-pass filter. Nothing changes about the components; only where you measure the output decides which frequencies pass. This is why RC pairs are the workhorse of simple audio and signal conditioning.
Finding the cutoff frequency
The turning point of an RC filter is the cutoff frequency, where the capacitive reactance equals the resistance. Setting Xc = R and solving gives f = 1 / (2 pi R C), the point where the output has fallen to about 70.7 percent of the input, or -3 dB. Below cutoff a low-pass filter passes the signal nearly untouched; above it the response rolls off at 20 dB per decade. You can find that crossover with this calculator by sweeping the frequency until the reactance it reports matches your resistor value.
Choosing real parts
Design usually starts from a target cutoff, then picks R and C to hit it. A common approach is to fix a convenient resistor, such as 10 kilo-ohms, and solve for the capacitor, since capacitors come in coarser value steps. Keep the driving source impedance well below R and the load impedance well above it so they do not shift the cutoff. Remember too that real capacitors carry tolerance and a little parasitic resistance and inductance, so a bench filter lands near the calculated cutoff rather than exactly on it.