RC Time Constant Calculator
One resistor and one capacitor make a clock and a filter at the same time. This is what yours does.
The time constant
τ = R × C is the time the capacitor takes to charge to 63% of the supply through that resistor. After five of them it's within 1% of full, which is the practical definition of "charged". 10 kΩ and 100 µF give a full second: that's a power-on delay built from two parts.
The same pair as a filter
Feed a signal through the resistor with the capacitor to ground and you have a low-pass filter that starts rolling off at fc = 1 ÷ (2πRC). Everything slower passes; everything faster fades. It's how you smooth a PWM output into something resembling a steady voltage, and why the values here show both numbers: same parts, two jobs.
Choosing R and C for the same time constant
Any pair whose product matches gives the same time constant, but they are not interchangeable. A large resistor with a small capacitor keeps current low and suits a high-impedance input, though it picks up noise and is loaded by whatever reads it. A small resistor with a large capacitor is stiff and quiet but draws real current and takes a physically larger part. For an ADC input, keep the resistor in the low tens of kilohms so the sampling capacitor still charges in time.
Smoothing PWM into a voltage
To turn PWM into a steady voltage, set the cutoff frequency at least ten times below the PWM frequency. At 1 kHz PWM, a cutoff near 100 Hz leaves visible ripple; near 10 Hz the ripple is small but the output takes a tenth of a second to follow a change. That trade between ripple and response is the whole design decision, and it is why motor control usually keeps the PWM and filters nothing at all.