What is the RC time constant and how do you determine it through an experiment?

[Physter]

Hi everyone http://img36.imageshack.us/img36/5721/wave7xq.gif .[/URL] I'm in a little bit of a mess and need some help with this lab write up. There's no way of getting in touch with my TA and my professor didn't prove to be that great of a help when I went to see him yesterday. Anyways, we did an experiment to determine the RC time constant. I guess it'd make sense for me to briefly go over the experiment and then mention the problems I'm having doing the writeup.

For the first part, we noted the times it would take for the current to fall whilst our single capacitor (62 microfarads) was charging. Then a graph of ln(current) as a function of charge time was plotted. For the second part, we did the same thing but only this time the data was for the discharge time of the capacitor. For part three, we did the same thing as part two (the discharge time) but only this time it ws for two capacitors (30 and 69 microfarads respectively) in series configuration . The last part was the same as part 3, only this time it was for the same two capactorss in parallel configuration. Using all this data and the graphs we plotted for each section, we're supposed to find the slope, C(charge), C(discharge), C(parallel), C(series) and of course the RC time constant http://img148.imageshack.us/img148/7246/smartass7jx.gif .[/URL]

Here's my graph for the charge time of a single capacitor http://img515.imageshack.us/img515/2216/graph1id6.jpg . I found the RC time constant by simply taking the value on the resistor and multiplying it by the value of the capactor (1000ohms*62microfarads). Is that right? http://img347.imageshack.us/img347/8900/unsure3ou.gif When it comes to finding C(charge) and C(discharge) off their graphs, I don't really know how. For C(parallel) and C(series), I simply used the rules for capacitors in parallel and in series (ie. C(parallel)=C1+C2+C3+...CN and C(series)=[1/C1+1/C2+1/C3+...1/CN]^-1) but again, I don't know how to determine these values off the graph http://img406.imageshack.us/img406/9710/sad0io.gif .[/URL]

Another thing, for our very first graph (ln(current) as a function of charge time for the single capacitor), we have to find the error on the slope and that's another thing I don't really know how to do. The error on our measurements for current was +/-0.2 microfarads and the error on the time measurements was +/-0.01 s.

Any help would be greatly appreciated http://img263.imageshack.us/img263/1031/sadangel0we.gif .[/URL]

 

[ELHEK]

Hey there! I've just currently done a electronics lab on testing the time constant(RC) of capacitors in networks. Your lab seems to be quite a bit more advanced compared to mine, but you can calculate the time constant by using method for a voltage vs time graph. the 63%37% method. I have no idea how it works but its worth having a look for on how it works. There is prob a good chance u know this already, anyways good luck.

 

[SGT]

The discharge voltage for a RC ciscuit is:
$$V(t)=V_0\cdot e^{-\frac{t}{T}}$$
Where $$V_0$$ is the initial voltage and T = RC is the time constant.
Knowing the initial voltage and the voltage at any time t, you can use logarithms to find T.