If I want to find the resistance(R) from a voltage(V) vs current(I) graph for a given wire using the relation tan Θ = ΔV/ΔI = R, do the scales on the axes need to be the same, independent of the units? Such as, "2mm on the x-axis=0.01A and 2mm on the y-axis=0.01V" or "2mm on the x-axis=0.01mA and 2mm on the y-axis=0.01V"? Or can the scales be different? Does this apply for all graphs where we use the slope or area of the graph to calculate things?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Suppose you have a straight line graph of voltage (kilovolt) and current (microamps) which passes through the origin and the point (6,kV, 5 $\mu$A) then the gradient of the graph is $\dfrac{6-0}{3-0}\,\dfrac {\rm kV}{\mu\,A} = 2 \times 10^9 \,\rm V/A = 2\, G\Omega$.
Note that there is no mention of the scale that was used to draw the graph and so you could have 1 cm = 1 kV and 2 cm = 1 $\mu$A, etc.
