1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find tme constant for discharging capacitor

  1. Mar 12, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi, I have a quick question about applying the RC time constant formula for a lab report. In the lab, we charged a capacitor to 20 V and then let them discharge, recording the voltage every 10 seconds, up to 240 sec. Now I was asked to graph the time vs. voltage in excel, fit an exponential trendline and obtain an equation.

    2. Relevant equations

    The equation I got from my line is: y = 19.89e-0.02x

    My lab manual gives the time constant formula as V = V0e-1/t , with t being the time constant.

    I have to use the experimentally obtained equation to calculate the time constant.

    3. The attempt at a solution

    I see the V0 is very close to 20, so that makes sense, but I don't understand how to combine the two equations to get the time constant. It seems that V should be the final voltage, but I have 24 values, all of which would give a different x. I'm confused how to proceed from here.
  2. jcsd
  3. Mar 13, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    I'm guessing you mean: $$V=(19.89V)e^{-(0.02)t}$$

    ... they mean: $$V=V_0e^{-t/\tau}$$ where ##\tau## is the time constant.

    The relation you have is for t=1s.

    You can use the data point at t=1s - very sloppy:don't do this.

    You can use the first few data points as an approximate straight line - the intersection of the best fit with the t axis will be close to the time constant.

    Best approach is to linearize the graph ... plot y=ln(V) against x=t.
    $$\ln|V|=\ln|V_0|-\frac{t}{\tau}$$ ... this is a straight line with intercept ##V_0## and slope ##1/\tau##. Find the slope.
  4. Mar 13, 2014 #3
    Another way of doing this is to recognize that, in the excel fit to your data, that 0.02 is the reciprocal of the time constant (are there any additional significant figures?). So the time constant should be about 50 seconds. This should be roughly the same result you get using Simon's linear plot.

  5. Mar 14, 2014 #4
    ^ That's it, I just had a brain freeze trying to derive the time constant from that exponent expression. Simon's method would produce a more precise value, but my manual specifically asked for an exponential trendline so I just did that and it gave me a close enough estimate for the purposes of this lab. Thanks both of you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted