I'm studying computer science and rarely come in contact with physics. However, as part of one assignment, I had to approximate a function based on the following measured data.

(the quality is kind of low - the graph is totally discrete)

$x$-axis is voltage in volts, $y$-axis current in amperes.

Now I have approximated the function that would fit this data, let's call it $f(x)$.

Now I have to calculate differential resistance in 0.4V and 0.48V using this function. If I'm not wrong and my internet research skills are not embarassing, I should make the derivative of f(x) - let's call it f(x)' and simply calculate the value of f(0.4)' and f(0.48)', which would give me the respective differential resistances.

Am I wrong?

  • $\begingroup$ Are you trying to estimate the differential resistance at two different points, or trying to estimate a single approximate value for differential resistance that's reasonable over the whole interval between the two points? $\endgroup$ – The Photon Jan 3 '17 at 19:03

You have got a graph of current $I$ against voltage $V$.

At a given current or voltage the resistance $R = \frac VI$.

The incremental or differential resistance at a given current or voltage is $\frac{dV}{dI}$.
So it is the reciprocal of the gradient of your graph.

You are given $I=f(V)$ so $\frac{dI}{dV} = \frac {df(V)}{dV}$ and the differential resistance is the reciprocal of that quantity $=\left (\frac {df(V)}{dV} \right )^{-1}$


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