# Find Resistance: Solve V vs. I w/ Tangent Line

• Richard Ros
In summary, the question asks for the values of R for seven points on a smooth curve of V vs. I. The formula R = V/I cannot be used, and instead, the marginal resistance of the lamp needs to be found using the slope of tangent lines or the equation of a best fit polynomial. The resistance of the bulb increases as it gets hotter, so experimental uncertainty should be taken into account when fitting the curve.

## Homework Statement

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

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.

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Last edited:
attachment is illegible

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

Richard Ros said:
Can you see it better now? I updated the attachment.

No, I still can't read it.

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

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.

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.

## 1. What is the purpose of finding the resistance using V vs. I with tangent line?

The purpose of finding the resistance using V vs. I with tangent line is to determine the resistance of a circuit or component by plotting the voltage and current data and drawing a tangent line at a specific point on the graph. The slope of the tangent line represents the resistance.

## 2. How is the tangent line drawn on the V vs. I graph?

The tangent line is drawn by selecting a point on the V vs. I graph and drawing a line that just touches the curve at that point. The slope of this line will be the resistance at that specific point.

## 3. What is the significance of finding resistance using V vs. I with tangent line?

Finding resistance using V vs. I with tangent line is significant because it allows for a more accurate and precise determination of resistance compared to other methods. It also helps to identify any non-linearities in the circuit or component.

## 4. Can the resistance be calculated using any point on the V vs. I graph?

No, the resistance can only be calculated using a point that falls within the linear region of the graph. This means that the voltage and current values must have a constant ratio and the graph should have a straight line at that point.

## 5. Are there any limitations to using V vs. I with tangent line to find resistance?

Yes, there are some limitations to this method. It assumes that the circuit or component being tested is linear, meaning the voltage and current have a constant ratio. It also requires accurate measurements of voltage and current, and can be affected by noise or fluctuations in the data.