Non ohmic graph and distance vs time graph

[sgstudent]

For a distance time graph, in order to get the instantaneous speed, I have to use a gradient. While for a non ohmic conductor, to find the resistance st s point I just use the formula R=V/I. Why is it so that I need not get the gradient at they particular point to find the resistance st that point whilst for the instantaneous speed, I have to use a gradient at that point?

Thanks so much for the help!

 

[technician]

On a distance time graph if you just took distance and divided by time you would get the average velocity.
You are quite correct... if you want the INSTANTANEOUS velocity you use the gradient.
If you want to know how far you will travel in the next minute you would use the instantaneous velocity (assuming it is not the same as the average velocity)
For a graph of V against I a point on the curve gives you a 'resistance' value if you do V/I. If the voltage then fluctuates and you want to know the current due to the fluctuation then you would use the gradient ΔV/ΔI to calculate the fluctuating current.
This is important when you meet characteristic curves of V against I (or I againstV) for such things as diodes, transistors, thermistors etc.
There may be a steady voltage with a fluctating (AC) voltage superimposed.
To calculate the effects of the superimposed AC you use the gradient.
Hope this helps

 

[sgstudent]

On a distance time graph if you just took distance and divided by time you would get the average velocity.
You are quite correct... if you want the INSTANTANEOUS velocity you use the gradient.
If you want to know how far you will travel in the next minute you would use the instantaneous velocity (assuming it is not the same as the average velocity)
For a graph of V against I a point on the curve gives you a 'resistance' value if you do V/I. If the voltage then fluctuates and you want to know the current due to the fluctuation then you would use the gradient ΔV/ΔI to calculate the fluctuating current.
This is important when you meet characteristic curves of V against I (or I againstV) for such things as diodes, transistors, thermistors etc.
There may be a steady voltage with a fluctating (AC) voltage superimposed.
To calculate the effects of the superimposed AC you use the gradient.
Hope this helps

But then why to find instantaneous speed why must I get the gradient while for non ohmic conductors why don't I need to use gradient? Thanks!

 

[Philip Wood]

It's a case of definitions. Resistance is defined by R = V/I. So you just divide V by I.

For a conductor which obeys Ohm's law, a graph of V against I is a straight line through the origin, so ΔV/ΔI at any point gives you exactly the same thing as V/I.

For non-ohmic devices (filament lamps, diodes and so on) the graph of V against I is not straight, so V/I is not a constant. [Nor does V/I usually equal ΔV/ΔI at a point.] Since V/I is not a constant for a non-ohmic device, the concept of resistance (defined as V/I) is far less useful for such a device: one might as well go back to the I against V curve itself, when doing calculations.

As the last poster pointed out, there are certain devices for which one is concerned with changes in V associated with small changes in I, for changes centred on a particular point on the V – I curve. In that case what we're interested in isn't V/I but really is ΔV/ΔI. This quantity is sometimes called 'slope resistance'. The reciprocal is 'slope conductance'.

For displacement – time (x – t) graphs, velocity is defined as [the limit as Δt approaches zero of] Δx/Δt because that's what we're interested in. [How fast was the car going when it crashed? There's very little interest in knowing x/t, the mean velocity since the journey started.

In general, things are defined as they are defined, because they're interesting and/or important when defined that way.