Try it
R charges C - Vout is the voltage building up across the capacitor
Understand the result
What's going on
A capacitor doesn’t charge instantly - it fills up like a bucket under a tap. A resistor in the circuit controls how fast that bucket fills. Put the two together and there’s a single number that describes the pace: the RC time constant, tau (τ).
The formula
τ = R × C
τ is in seconds when R is in ohms and C is in farads.
Show the derivation, mnemonic, and worked example
Build it up
A bigger resistor is a narrower tap - it slows the flow of charge into the capacitor. A bigger capacitor is a bigger bucket - it takes more charge to fill to the same level. Slow the flow or grow the bucket and either way, filling takes longer. So the time constant just grows with both.
In one time constant, a charging capacitor reaches about 63% of its final voltage. After roughly five time constants (5τ), it’s considered fully charged for practical purposes.
Worked example
Worked example
R = 10 kΩ, C = 100 µF
τ = 10,000 × 0.0001
τ = 1 second
