but Ohm's Law states that the voltage changes also because of the characteristic of the conductor (Resistance).
Actually, Ohm's law does not state that. Ohm's law is just a relationship between - in this case - 3 parameters: Resistance $R$, current $I$ and voltage $V$.
$$V=RI$$
But while it is the relationship between them, it does not state which ones are dependent and will change when another one changes. That depends on the situation.
In the case of a battery connected to a simple circuit, we know that the voltage is constant. Regardless of the resistance in the circuit, the voltage is always, say, 5 V across the two battery terminals. This is true when not connected (open-circuit, effectively infinite resistance), when connected (some specific value of resistance) and when short-circuited (effectively zero resistance).
The voltage is constant and doesn't depend on the resistance that happens to be in the way. So, when looking at Ohm's law, what is then changing, if not $V$? Mathematically, you are right that something else must change when $R$ changes. But it doesn't have to be $V$ - it can also be $I$. And it is.
Think of $V$ as the "pressure" that "pushes" on charges.
- In the open-circuit case, they are being pushed with 5 V, but they still can't move because there is no conducting path - infinite $R$ but zero $I$. Ohm's law obeyed.
- In the connected case, they are being pushed still with 5 V, and they flow with whichever current $I$ that fulfills Ohm's law. $R$ limits and alters $I$, not $V$.
- In the short-circuit case, they are still being pushed with 5 V and this time nothing stops them. They speed up and up and up. At any flow speed (current), the 5 V pushes them faster to gain higher speed, which continues forever (or until the heat generated melts the wire). $R$ is zero and $I$ infinite - Ohm's law obeyed.
In general, be careful when reading a mathematical formula. It only shows a relationship between parameters - it doesn't show which of them that are dependent and which that are fixed. That depends on the particular situation.
The relation $$V=IR$$ also holds for a non-ohmic conductor (resistor). The only difference to an ohmic conductor is that the resistance $R$ is not constant but can depend on current $I$, voltage $V$, or even on time.
Best Answer
The resistance $R$ of a circuit element as shown in your graphs is
$R = \dfrac{\text{potential difference across circuit element}}{\text{current passing through circuit element}} = \dfrac VI$
For the graphs that you have drawn the value of the resistance will depend on the current passing through the circuit element.
For the left hand characteristic the resistance decreases as the current increases and the right hand characteristic the resistance decreases as the current increases.
Note that for the right hand characteristic an increase in current produces a decrease in the potential difference
It is often more use to know what happens when the current or voltage changes by a small amount around a given value of current or voltage, these sometimes being called the working current or voltage.
That is when the gradient of the curve about the given value of current or voltage is measured to give the incremental resistance, small signal resistance, differential resistance etc where
$R_{\rm incremental} = \left (\dfrac {d V}{dI} \right )_{\text {V,I fixed}}$
Now for a small change in the current $\Delta I$ about that given value of current or voltage the change in the voltage $\Delta V$ is
$\Delta V \approx R_{\rm incremental}\,\Delta I = \left (\dfrac {d V}{dI} \right )_{\text {V,I fixed}}\, \Delta I$