Graphical or calculation solution. Which is better? Ohms law

[Barclay]

Homework Statement

A student is calculating the resistance of a piece of fuse wire. He takes 5 readings on the voltmeter and ammeter for different settings of a variable resistor.
He decides that instead of measuring the gradient of the graph to calculate the resistance, it would be okay to use the formula R = V/I for each pair of measurements and then finding the mean.

Question is : Why is calculating the gradient of the graph a better method?

Homework Equations

V = IR

The Attempt at a Solution

The graph method is better because we can see any outliers instantly i.e points on the graph that don't fit the line/curve so can be ignored (assumed to be errors).

Is that an okay answer? Any other suggestions please. Thank you.

 

[BvU]

Very good argument, but there's another, probably more relevant in this context.
Difficult to help you without giving away, but: do you think the resistance to be measured is relatively big, or is it expected to be rather small ?
And: sketch the setup of the measurement; it might give you an idea...

 

[Barclay]

Difficult to help you without giving away

Would be nice if someone just gives up the answer. You don't know how much brain ache physics causes some of us.

Anyway results of experiment are:

PD = Current = Resistance (Ohms)
0 V = 0 mA = 0
1 V = 88 mA = 11.36
2 V = 177 mA = 11.29
3 V = 275 mA = 10.9
4 V = 363 mA = 11.01
5 V = 451 mA = 11.08

[ I took mA to mean 10^-3 so 451mA is 451x10^-3 ]

So BvU I can't see why a graphical method is better than calculation. (There aren't any outliers).

Or maybe its something to do with the 0mA and 0 Ohms values. These can be ignored on the graph and are the outliers as the wire warms up

 

[BvU]

Would be nice if someone just gives up the answer

I'm feeling with you, but just giving the answer generally ruins the learning experience and that's not what PF standsd for.

In this case I think you've done well. So some leniency on my part (I hope I don't get kicked out of the forum now, so don't tell anyone ):

My vague reply was based on the possibility that the graph would show a line that doesn't go through the origin. It does go through the origin ( I don't think you mean the resistance is really zero there ... and I wonder if 0,0 is a measurement with equal weight as the others).

I figured a piece of fuse wire would have a lot lower resistance, so the connecting wires might play a role. Apparently wrong.

Fact remains that a graph is better than just taking the mean: as you say, it's a lot easier to detect outliers. It's also a good way to check if the supposed relationship is really linear, whether origin is on the graph or not.

And later on, once you have learned how to do statistics and determine the error in the results, you can also check those outcomes.

And the results will be even better if the range of your independent variable is maximum. Here it means that you can repeat the measurements after reversing the direction of the current : that way your plot goes from -5 to +5

But again: that's for later.

Good luck with the headache ! Just keep going and it will go away, I hope

 

[Barclay]

Thanks BvU

So final answer would be my comment on the outliers and your comment "It's a way to check if the relationship is linear" What is the relevance of knowing whether the "origin is on the graph or not" ?

 

[BvU]

In the dark ages we had voltmeters that needed some current to make a needle deflect and ammeters that had some small resistance; depending on your circuit that could cause the line to miss the origin...
Nowadays I suppose a possible offset can give a similar result.

Generally, assuming the line goes through 0,0 is one thing; checking that it does so is better.