I've done an experiment to study a capacitor's discharge time and calculate an unknown capacitor's capacitance.
With the help of an oscilloscope, I measured the time it took for the capacitor's voltage to reach half the maximum voltage. I repeated this procedure for different resistors and I got this graph:
I've spent hours trying to explain the coordinate at $R=0$ ($b=-0.8369$), but I can't come up with a plausible explanation!
Curve fitting for data is valid only when both the quantities being considered have any physical meaning. Also, curve fitting must be taken with a pinch of salt. By fitting and extending a curve, you are only obtaining a likely value, which often, is not the right value. A diode's I-V characteristics is such an example where extending the linear region beyond a certain point would not really reflect on what actually happens when you conduct the experiment. However, in your case, it is a case of bad fitting. When I say "bad fitting", extending it to $R=0$ does not yield right answers. However, it is possibly good enough for $R=3000$.
As one of the comments to the OP's question said, if you take more samples, the expected tension at $R=0$ will probably approach zero as well.
Edit: Here is some more information -
A curve fit is a curve that approximately represents the data points you have. The emphasis is on approximately and not accurately. The accuracy increases with the number of data points you have already, although that might be an oversimplification. So in your case, the number of data points is simply not sufficient. As an example, for the $R=7000$ case, your line is clearly missing the point. It is close enough, but surely not exact. Same thing at $R=0$. Here, however, the approximation led to physically infeasible values.
Assuming you mean "voltage" when you say "tension", a capacitor discharges with
$$ V(t) = V_0 \cdot e^{-t/(RC)}$$
You have determined the time $t_{50}$ to the half way discharge point, i.e. $e^{-t_{50}/(RC)} = 0.5$. We can solve for $C$
$$C = \frac{t_{50}}{R \cdot ln(2)} $$
You can use this formula to create a capacitance from each individual measurement that should be a constant (i.e. a straight horizontal line), which can do curve fit, or simply take the mean. If it's NOT a straight horizontal line (roughly), than something is wrong with your experiment.
Looking at $R=0$ is not helpful, since the discharge time will also be close to zero so the get $0/0$ which is undefined and any small type of noise or parasitic effect will throw off your data.
