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graph of I against V

Hi guys
there's this question i'd like to share idea about is that the current I through a wire of resistivity P varies with the length L, area of cross-section A and pd V, in accordance with the equation I=VA/PL .
If i want to sketch the graph of i against pd for the equation above, would it be directly proportional from the origin or only proportional which is a straight line but not from the origin. I'm guessing it's directly proportional but not too sure.
thanks for any help
(edited 8 years ago)
Original post by Alen.m
Hi guys
there's this question i'd like to share idea about is that the current I through a wire of resistivity P varies with the length L, area of cross-section A and pd V, in accordance with the equation I=VA/PL .
If i want to sketch the graph of i against pd for the equation above, would it be directly proportional from the origin or only proportional which is a straight line but not from the origin. I'm guessing it's directly proportional but not too sure.
thanks for any help


Just check, if V = 0, then l = 0.
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Alen.m
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Original post by EricPiphany
Just check, if V = 0, then l = 0.

How should i check that? There are no numbers for varaibles. It's more like a graph question to see if im good at showing the relationship between two varaibles on a graph
Original post by Alen.m
How should i check that? There are no numbers for varaibles. It's more like a graph question to see if im good at showing the relationship between two varaibles on a graph


Keeping k=Aρl≠0k=\dfrac{A}{\rho l}\not = 0 constant, then I=kVI = kV.
So directly proportional.
V=0⇒I=0 V=0 \Rightarrow I=0
(edited 8 years ago)
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Like how do you know the constant(K)=A/PL , couldnt find anything on my notes . Basically everytime you want to see if two varaibles are proportional or not you should check if they both give you zero?not any other value?
When you're doing an experiment you deliberately vary one variable (the independent variable) and measure the resulting change in another variable (the dependent variable). you might think of these as input and output.

You try as hard as possible to keep everything else constant.

in this experiment it seems most likely that you'll have PD as the independent variable and I as the dependent variable... so you'll try and keep A, L and rho constant - probably by using the exact same piece of wire at each voltage.

(VA)/(rho L) = V (A/(rho L)) <- everything in the brackets is constant, so we can replace with k
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Original post by Joinedup
When you're doing an experiment you deliberately vary one variable (the independent variable) and measure the resulting change in another variable (the dependent variable). you might think of these as input and output.

You try as hard as possible to keep everything else constant.

in this experiment it seems most likely that you'll have PD as the independent variable and I as the dependent variable... so you'll try and keep A, L and rho constant - probably by using the exact same piece of wire at each voltage.

(VA)/(rho L) = V (A/(rho L)) <- everything in the brackets is constant, so we can replace with k

Great explanation for the constant thanks. Would also explain what is the best way to spot the relationship between two varaibles in a equation to plot the graph accurately for example should i put zero for one varaible in a equation to see if the other one gives me zero or not? If it does then they're directly proportional but how about if it dosent for example put instead of one zero and the other one gives 2
Original post by Alen.m
Great explanation for the constant thanks. Would also explain what is the best way to spot the relationship between two varaibles in a equation to plot the graph accurately for example should i put zero for one varaible in a equation to see if the other one gives me zero or not? If it does then they're directly proportional but how about if it dosent for example put instead of one zero and the other one gives 2


Well if you're graphing a theoretical relationship plug in some values of V into your equation and see what current you come out with.

worth noting that the equation of a straight line (any straight line) is y=mx+c
m is a constant, the gradient.
the +c (if it's there) tells you that the line misses the origin (0,0) because when x=0, y=c.

if you're graphing an experimental relationship you'll have to actually do the experiment and plot some points.
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Original post by Joinedup
Well if you're graphing a theoretical relationship plug in some values of V into your equation and see what current you come out with.

worth noting that the equation of a straight line (any straight line) is y=mx+c
m is a constant, the gradient.
the +c (if it's there) tells you that the line misses the origin (0,0) because when x=0, y=c.

if you're graphing an experimental relationship you'll have to actually do the experiment and plot some points.

the reason I'm asking is because im not really good at sporting weather a graph is proportional or directly proportional.what's the difference between these two?i know the fact that directly proportional goes through origin but how about only proportional?what the graph looks like when two variables are only proportional?is there anyway you can spot the relationship between two variable as proportional from an equation?thanks for your time
Original post by Alen.m
the reason I'm asking is because im not really good at sporting weather a graph is proportional or directly proportional.what's the difference between these two?i know the fact that directly proportional goes through origin but how about only proportional?what the graph looks like when two variables are only proportional?is there anyway you can spot the relationship between two variable as proportional from an equation?thanks for your time


if it rearranges to y=mx then it goes through the origin because anything multiplied by 0 is 0

if it rearranges to y=mx+c then it can't go through the origin because when either x or y is zero, the other cannot be zero.
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Original post by Joinedup
if it rearranges to y=mx then it goes through the origin because anything multiplied by 0 is 0

if it rearranges to y=mx+c then it can't go through the origin because when either x or y is zero, the other cannot be zero.


can i just conclude if an equation can be written in the form of y=mx is directly proportional and if it can be written in the form of y=mx+c is only proportional
Original post by Alen.m
can i just conclude if an equation can be written in the form of y=mx is directly proportional and if it can be written in the form of y=mx+c is only proportional


that's correct :thumbsup:
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Original post by Joinedup
that's correct :thumbsup:


thanks

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