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Discharging a Capacitor and the Time Constant

A capacitor discharging through a resistor loses charge at a rate set by the charge still on it, so voltage, charge and current all fall exponentially. The product RC is the time taken to fall to about 37 per cent.

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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.

Good to know

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

Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.

Where it sits

Where this leads

Jobs that lean on this skill. Follow one to see everything it is built on.

Then practise

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.

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Discharging a Capacitor and the Time Constant · Science, ages 17 to 18 · LightMySky