Solved example: (Ohm's law graph)

we have a graph of voltage versus current for two materials and the question is which of the two materials has higher resistance in a previous video we saw that when the voltage versus current graph of any material is a straight line passing through the origin then that material obeys Ohm's law now notice that both the materials have the graph of straight line passing through the origin so both materials obey Ohm's law so we need to check now which of them has a higher value of resistance to do this let's quickly recover Ohm's law was Ohm's law says that voltage V equals I current I times the resistance R and to calculate the resistance we can divide by current on both sides so if we do that we'll get V over I equals R so notice we can calculate the resistance of a material by calculating the ratio of the voltage and the current so whichever material has a higher value of V over I will have a higher value of resistance so all we need to do is check which of these two material has higher values of V or I from the graph but how do we do that because the values are not mentioned in the graph well there are a couple of ways we can do this one way is we can pick a point on the graph for both these materials such that they have the same value of the current so that they would have the same denominator and find out which of them has a higher value of voltage higher numerator the one which has the higher numerator will have the higher value of R so that's one way pick same.i and check which has more voltage another way would be pick points on this graph such that they have the same value for voltage so same numerator now figure out which of them has a lower value of current because smaller the denominator more will be the value of V or I so you know you can choose any method and figure out which of them has higher resistance so it would be a great idea to pause the video and see if you can you know try and do this yourself alright I'll pick the one which has the same current so let me pick some random value of current over here and let's now pick points on these two graphs where they have this much current so to do this we'll just have to draw a vertical line and now this point on the graph represents this much current and this point on the graph also represents the same current so these two points now represent the same value of the current now all after check is which of them has a higher value of voltage well let's see if you look at this one notice this has a voltage value which is somewhere over here and if you look at this one it has a voltage value which is somewhere over here clearly the first one has a higher voltage compared to the second one for the same current in other words the first one has the higher ratio and so the first one has a higher resistance so we can say from this the resistance of the first material must be larger than the resistance of the second material and if you had picked the same voltage and checked which has less current you would have gotten the same answer you can go ahead and pause the video and try that to convince yourself alright let's do another one again we have to calculate which of the two has higher resistance but this time the voltage is Fault along the horizontal and the current is plotted along the vertical but but that shouldn't confuse us because the steps are still the same so pause the video use the same steps and see if you can get the answer all right again I will pick a point where the current is the same so let's take let's say let's let's assume the current is somewhere over here let's pick point on these two graphs where the current is the same so if I do horizontal this time I draw a line horizontally like this well since this line doesn't meet over here let's pick a point somewhere down okay right so now we have this point and this point both the points correspond to the same value of current this much value of current and again after check which of them has a higher value of voltage so let's see if we drop a vertical line the voltage for the first one is somewhere over here the voltage for the second one is somewhere over here clearly we can see the second one now has a higher value of voltage this is the higher value of voltage compared to the first one and so the second one has more voltage compared to the first one for the same current and as a result this time it's this one that has a higher resistance and so our two this one has a higher resistance compared to our one compared to our one so regardless of which axis this voltage and which axis is current if we pick a point where the current value is the same for both graphs and figure out where the voltage is more we can easily find where which which of them has a higher resistance