Help with FaraDay’s law graphsWatch

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Thread starter 9 months ago
#1
Hi, i don’t understand this point:

“/\ y / /\ x is the change in y divided by the change in x. As /\ y and /\ x get smaller, /\ y / /\ x gets closer to dy/dx and for a straight line graph (as shown) /\ y / /\ x and dy/dx are the same”

I know dy/dx is the gradient / differentiated version etc, but I thought that was the same as /\ y / /\ x as that surely is also the gradient. So why is the question saying that they are usually not the same until /\ y and /\ x get smaller?

Also the diagram they are referring to is one of the two shown - it is hard to tell as they are both straight line graphs!
0
9 months ago
#2
(Original post by LesliA1998)
Hi, i don’t understand this point:

“/\ y / /\ x is the change in y divided by the change in x. As /\ y and /\ x get smaller, /\ y / /\ x gets closer to dy/dx and for a straight line graph (as shown) /\ y / /\ x and dy/dx are the same”

I know dy/dx is the gradient / differentiated version etc, but I thought that was the same as /\ y / /\ x as that surely is also the gradient. So why is the question saying that they are usually not the same until /\ y and /\ x get smaller?

Also the diagram they are referring to is one of the two shown - it is hard to tell as they are both straight line graphs!
Delta is used to signify the gradient between two points on a graph. At GCSE and A-level, all laws and rules are idealised with no allowance for energy losses in reality. Graphs are always straight line or follow exact curves.

In reality (engineered materials / devices), nothing is ever that simple. Straight lines are approximations and curves deviate from perfect. Which is why the delta gradient between any two points is always an average of all measurements between those points.

The differential dy/dx is stated for the limiting condition where the difference in both X and Y distances approach zero. i.e. The dy/dx gradient is only valid for any given point on the curve.
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