p and L are related by the equation
p=RA/L
where all the other quantities in the equation are constant. How do I work out the gradient of a graph in which ñ is plotted against 1/L?
To work out the gradient of a graph where ɲ (ñ) is plotted against 1/L, you need to use the equation p = RA/L and rearrange it to solve for ɲ.
Let's start by rearranging the equation:
p = RA/L
Lp = RA
Now, let's isolate ɲ by dividing both sides of the equation by A:
ɲ = RA/A
ɲ = R
Now we have the equation for ɲ in terms of R.
To find the gradient of the graph, you need to find the change in ɲ divided by the change in 1/L.
Δɲ / Δ(1/L)
This is the definition of a gradient.
When you have plotted the graph with ɲ on the y-axis and 1/L on the x-axis, you can choose two points that lie on the graph. Let's say these points are (x1, y1) and (x2, y2), where x represents 1/L and y represents ɲ.
Now, you can calculate the change in ɲ and the change in 1/L:
Δɲ = y2 - y1
Δ(1/L) = x2 - x1
Finally, you can calculate the gradient by dividing the change in ɲ by the change in 1/L:
gradient = Δɲ / Δ(1/L) = (y2 - y1) / (x2 - x1)
This will give you the numerical value of the gradient of the graph.