High School Exponential formula for Excel sheet

[MrNewton]

TL;DR

I have 2 values. #1 around 3.25V, #2 around 2.82V. I place them in excel, but want to make a graph with an exponential decrease between the 2 points (like a capacitor discharging) like attachment. What formula can i use in excel to make this curve?

Hello,

i am testing batteries for a project of mine. I first measure the voltage on the battery (OCV, Open Circuit Voltage), and then i place a load resistor over the battery. This results in a voltage drop with a exponential decrease in voltage like in the image. But i am working with a microcontroller, and i am using the 10 bits AD converter to read the voltage with the microcontroller. So with each load, i measure 2 voltages. #1 i measure right before 0.5s, so around 3.25V. The other point where i measure is at 2.5s, around 2.82V. With those values you can calculate the internal resistance of the battery. BUT: with those 2 points i cannot draw a curve like below. My question: How can i draw this curve in Excel, with only 2 values. I don't need the line of the curve to be exactly right, i just want the image of an exponential decrease in voltage from the OCV to the load voltage.
I do not want to use the ADC to measure all the values between 0.5 and 2.5 seconds because that would take a lot of memory in my case.https://www.physicsforums.com/attachments/265171

 

[DrStupid]

It seems you are looking for

$U = U_0 \cdot \exp \left( { - k \cdot t} \right)$

with

$k = \frac{{\ln \frac{{U_1 }}{{U_2 }}}}{{t_2 - t_1 }}$

$U_0 = \frac{{U_1 }}{{\exp \left( { - k \cdot t_1 } \right)}}$

 

[kuruman]

I cannot see your picture. Can you?

I don't need a picture to ask you this, how did you choose the particular values of 0.5 and 2.5 s and why only two? Since you only need a rough estimate of the exponential decay, it seems to me you will need as many measuring times as parameters in your model. It seems to me that the model you need to fit to is $V(t)=V_0~e^{-t/\tau}+V_{\infty}$, where
$V(0)$ = voltage at time $t=0,$
$\tau$ = decay time constant,
$V_{\infty}$ = steady state voltage.

The key question here is, at t = 2.5 s has enough time elapsed for the circuit to have reached the steady state voltage at 2.83 V? I would recommend measuring $V_{\infty}$ separately, perhaps with a voltmeter, several minutes after adding the load. That way you will know its value and guide your thinking about what to do next.

Plan A. If $V_{\infty}$ is considerably less than the second measurement of 2.83 V, then you have a good set of points to do an exponential fit to the model I suggested. On Excel you would plot $V(t)-V_{\infty}$ vs. $t$ and ask it to do an exponential fit. That will give you $V_0$ and $\tau$.

Plan B. If $V_{\infty}$ is close to 2.83 V (how close is "close" depends on the precision of your measurement), then you need to adjust the timing of your two measurements so that the second measurement is considerably more than 2.83 V. Then proceed as in Plan A.