Prove Voltage should be linear function of position

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Giving that: V(x)=Cx
Express the answer in terms of wire length L, battery voltage Vin the variable x and any numerical or physical constant. C should equal to 1.3594 which is the slope of my volage vs distance graph.

This is what i got so far. Not sure if it is correct.
V=iR -> V=(i*(rho)*L)/A so therefore my C is i(rho)/A and L=x

Am i going in the right direction?
 

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  • #2
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Well, obviously C = Vin/L.
So V(x) = Vin*x/L.
I can't see what for you need the numerical value, or a graph.
Is this really college level?
 
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avs
yea it's for a physics 2 lab.
 
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HallsofIvy
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I'm puzzled by your titling this "Prove Voltage should be linear function of position" and then imediately saying "Giving (Given?)that: V(x)=Cx"

If the problem is to prove something, then you wouldn't be "given" it!

Since this is for a physics LAB, I suspect that you were asked to measure voltage versus length of wire in the laboratory, then graph the data. "Proving" (not in the mathematical sense) that voltage is a linear function of length is just a matter of observing that the points tend to lie along a line.

Since you say that you have already done that and found that the slope of the line is 1.3594, you know that you can write V(x) as
V(x)= 1.3594x+ V0 (V0 is the voltage when x= 0. If I understand your experiment correctly, that should be Vin.)

You are asked to "Express the answer in terms of wire length L, battery voltage Vin the variable x and any numerical or physical constant."

Okay, what is the voltage when x= L, then entire length of the wire?
If you call that Vl, then you should have (Vl- Vin)/L= slope= 1.3594.
 

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