What a learner can do afterwards
- Predicts the voltage after a stated number of time constants and reads RC off a decay curve
- Uses the exponential form to find either a remaining charge or an elapsed time
- Plots the natural log of voltage against time and takes RC from the gradient of the straight line
1 · Read
A resistor in series with a capacitor sets the pace of discharge. The time constant tau equals R times C, in seconds for ohms times farads. After one constant the voltage has fallen to about 37 percent. After five it is effectively zero.
Discharge runs on an exponential: voltage equals start voltage times e to the minus t over R C. A 10 microfarad capacitor through a 100 kilohm resistor gives R C equal to 1 second. These fixed fractions predict the voltage after any count of constants with no heavy lifting.
Take the natural log of voltage and plot it against time to get a straight line. Its gradient is minus one over R C, so R C drops out with a ruler. Keep units strict: convert milliseconds and microfarads before they meet.
Price discharge in time constants, trust the 37 percent rule, and read R C off logged data.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.