Finding resistance from V vs. I curve using tangent lines

[Richard Ros]

Homework Statement

Using the smooth curve for V vs. I and find values for R for the seven values of V and I.

Homework Equations

P = VI
R ≠ V/I

The Attempt at a Solution

I got the slope of the tangent line and got .002Ω for each point... Doesn't seem like a correct value. Can someone tell me how to get R. It is hinted something about the tangent line. I can't use the formula R = V/I for some reason stated on the paper.

 

[phinds]

attachment is illegible

 

[Richard Ros]

Can you see it better now? I updated the attachment.

 

[phinds]

Can you see it better now? I updated the attachment.

No, I still can't read it.

 

[Richard Ros]

Okay. I've zoomed in the image if you are having a hard time reading it.

 

[haruspex]

I find this question bizarre. To the best of my knowledge, R = V/I by definition. They seem to want you to find the marginal resistance, i.e. ΔV/ΔI for some small change in voltage, but that is not the resistance of the lamp.

 

[Chestermiller]

The resistance of the bulb increases as it gets hotter. As haruspex points out, what they seem to be looking for here is the incremental resistance dV/dI (since the relationship between V and I is non-linear).

Your data has some experimental uncertainty to it, so you need to fit a smooth curve to the data (of course, passing through the origin). You can use a French curve to do this, or you can do it with a graphics package to obtain a best fit using a low order (say 2 or 3 degree) polynomial. If you do it using a French curve, you can draw tangents to the smooth curve and obtain dV/dI from the slope of the tangent lines. If you do it with a graphics package, the package will provide the equation for the best fit polynomial, and you differentiate to get dV/dI.