
ITERATIVE SIMULATION OF CAPACITOR DISCHARGE

Over the last few years, many syllabuses have started to specifically state that candidates should have encountered the use of spreadsheets to mathematically model capacitor discharge. It's then quite common for questions to be asked about making these more accurate by, for example, using smaller time increments in the model.
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To save you the effort, here's a file which not only does it all for you but also plots the iterative method's results alongside the usual exponential equation's results for comparison. Your pupils should then be able to see how the two relate to each other. You can also change the time increment and instantly see how the iterative model's accuracy changes.
One feature of this graph that I would suggest you point out explicitly is that the initial rate of decay of charge in both models is the same, but the iterative method assumes this rate remains constant over whatever Δt is being used. By comparison, the exponential decay equation adjusts the rate of decay over infinitesimally small time periods because its derivation is based on integration. Understanding this can lead to a good explanation of the dice half-life problem.
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Derivations of the exponential capacitor decay equation are fairly common, but here's one I wrote that is aimed at school-level (though it only makes full sense if integrating 1/x has been covered):