As the lab capacitor discharged, it did so ever more slowly, and because of this you...
As the lab capacitor discharged, it did so ever more slowly, and because of this you had to some point simply call an end to data collection even though the capacitor was obviously still discharging. This is because with V = V0e-t/RC, it mathematically takes an infinite time for a capacitor in an RC circuit to fully discharge. Since one cannot measure forever (nor is the equipment accurate enough to do so), is is useful to know exactly how discharged the capacitor is at some given time so that one can estimate experimental errors. So, how many time constants does it take for a capacitor to discharge to less than 1% of its initial voltage?
Homework Answers
Using the eqn given,
V = Vo*e-t/RC
0.01*Vo = Vo*e^(-t/RC )
0.01 = e^(-t/RC)
100 = e^(t/RC)
ln(100) = t/RC
2*ln(10)*RC = t
=> t = 4.61 RC
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