Question

Graph showing the variation of current versus voltage for a material GaAs is shown in the figure. Identify the region of:
(1) Negative resistance
(2) Where Ohm’s law is obeyed

Answer 1

Hint: As a first step you could recall the ohm’s law and hence understand the relation of resistance with voltage and current. A region is said to obey ohm’s law when the current linearly with the increase in voltage, identifying such a region from the graph will give you an answer for the second part. Now for negative resistance, look for regions where the current decreases linearly with voltage.

Formula used: Ohm’s law,
$V=IR$

Complete answer:
In the question, we are given a graph showing the variation of current with voltage for the case of a GaAs material and we are asked to find the region that has negative resistance and also to identify the region that obeys Ohm’s law.
In order to identify these regions all you have to possess is clarity on the concept of Ohm’s law. Let us recall Ohm’s law which states that voltage across two points is directly proportional to the current flow across them, that is,
$V\propto I$
$\therefore V=IR$
Where, R is the resistance which is also the proportionality constant here.
For the first part of the question, where we are asked to find the region with negative resistance, we should look for the region with negative slope. Remember that, the resistance is the opposition to the flow of current. That is, the region where the current is decreasing with increase of voltage will have negative resistance. From the given graph region DE has negative resistance as per the above conditions.
Now for the second part, we have to find the region that obeys ohm’s law. A region where the current increases linearly with the increased voltage obeys ohm’s law. Hence region BC obeys ohm’s law.
Therefore, we found that the region DE has negative resistance and region BC obeys ohm’s law.

Note: We should note that the resistance here is constant for a circuit. It doesn’t change its value with increase or decrease in current as per Ohm’s law. The vector form of Ohm’s law is given by,
$J=\sigma E$
Where, J is the current density, E is the electric field and $\sigma $ is the conductivity.