Firstly, what is the significance of tau (time constant) in an RC circuit?
secondly, when charging and discharging capacitors in RC circuits, what is the significance of half the tau (time constant) value?
more specifically, what is the significance of the value tau_1/2 = RC ln2?
if you can help, you're awesome!
secondly, when charging and discharging capacitors in RC circuits, what is the significance of half the tau (time constant) value?
more specifically, what is the significance of the value tau_1/2 = RC ln2?
if you can help, you're awesome!
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The time constant is precisely R x C and is measured in seconds (perhaps surprisingly, but work it out!).
It appears in the equation of how charge flows off a capacitor in a RC circuit, specifically in the term e^ -(t/tau), or if you like e^ -(t/RC).
More generally it tells you how quickly the current decays to 1/e (or about 37%) of its original value. As a rough rule it takes about 5 tau for the decay to have completed, or 10 tau if you want to be absolutely sure all is finished.
The pattern of decay is exactly the same as radioactive decay, and the link between them is that the half life = tau x ln(2), which seems to be what you have above.
And I'm not awesome - I've just read a few more books than you on this subject.
It appears in the equation of how charge flows off a capacitor in a RC circuit, specifically in the term e^ -(t/tau), or if you like e^ -(t/RC).
More generally it tells you how quickly the current decays to 1/e (or about 37%) of its original value. As a rough rule it takes about 5 tau for the decay to have completed, or 10 tau if you want to be absolutely sure all is finished.
The pattern of decay is exactly the same as radioactive decay, and the link between them is that the half life = tau x ln(2), which seems to be what you have above.
And I'm not awesome - I've just read a few more books than you on this subject.