Voltage (V) Current (mA)
0 0
1 20
2 30
3 65
4 98
5 174
6 280
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84 comments:
Firstly by analysing the values given I can speculate that the graph is indeed not a straight line. I used Microsoft Exel to generate this graph and it produced an exponential curve.
Also what could have been done is to look for trends in the gradient of the values given. If the gradient was constant between two sets of points then the graph would indeed be a straight line. However the gradient is not constant so it is a curve. When it is generated specificlly an exponential curve would have been observed.
Straight line graphs tend to "give themselves away" There values for the x axis and the y axis tend to increase uniformly eg.
x- 1,2,3,4,5
y- 10,20,30,40,50
There are several ways to identify what kind of graph would be generated fron a set of co-ordinates. Ultimately though it all simplifies down to the gradient of the graph. After all the gradient of a graph would determine if it is a curve or straight line.
Does anybody know any other ways to identify if a graph, when generated would produce a straight line or a curve without plotting it. I ask this because it is always useful to have an idea of the graph we expect before plotting it. Would not you all agree?
Is there anybody on this blog right now to answer my question? I get the impression that i am speaking to my keyboard.
I see someone has erased there commemt. Have you decided to andwer my question?
I have a very interesting question or so i think of it, here goes:
Remember there are ways of spotting a straight line graph and ways to spot a curved graph. How about a graph that has both a line and a curve? Are there ways of determining a graph of this sort without plotting?
An addition to my previous comment:
If my memory serves me well remember in the Hooke's Law experiment remember the graph generated from the experiment produced a straight line initially and ended in a curve.I put this example so it might help in the thought process.
Have a go at this one:
With reference to my previous comment of the Hooke's law experiment and the graph generated. How would you have found the gradient of this graph.
Think about the following and share your thoughts:
1. Would the graph have one gradient?
2.Would the graph have two gadients?
3. Would it be possible to find the gradient at all?
4. OR is all of the above not valid and requires a change in syntax.
Fancy a go at this one:
How are graphs that have both a straight line and a curve are applied to real life. Is there any real life application? What can we say is the application of the gadient(s) in this instance then?
Contemplate upon this and share your thoughts:
In an industrial plant a very important and potentially dangerous mixing of two chemicals A and B process is being carried out.
Such that 1 unit of A mixes with 10 units of B.
2 units of A mixes with 20 units of B.
3 units of A mixes with 30 units of B. (and so on)
From the control room the operator is observing the progress of the process from a graph generated on the computer which recieves its data from sensors in the mixing tanks. The graph generated produces a straight line.
SUDDENLY the graph generated begins to curve.
1. If you are the operator what should you interpret from this change in the graph (if anything)
2. Should this be of any concern?
3. What could be done to fix the situation?
ADDITION TO MY PREVIOUS COMMENT:
Lets say that due to some minor leaks the process occasionally generates a curve then reverts back to a straight line. How then from using graphs alone can we determine if there is a problem with the mixing process.
1. Is it possible at all.
2. How can we minimise the curves generated in the graph. Can we practically stop curves generated on the graph.
3. REMEMBER chemicals and eqipmemt costs money. So an economical and practical solution should be generated.
TWO THINGS TO NOTE CAREFULLY:
1. ANSWER MISS QUESTION FIRST BEFORE CONSIDERING MY QUESTIONS.
2. I am not posting challenges I genuinely do not know the answers to my questions and would appreciate if you shared your knowledge with me in discussion.
THANK YOU.
Graphs are very interesting and so useful. We use graphs everyday. You may or may not know it but graphs are used to save the lives of people, Keep order, manage tasks of global proportions, help interpret past information and how to apply it presently, foresight on errors we would not normally see that could even have cost human lives, it also can leave data so that future individuals would not make the same mistakes twice. We as Mathematics students should appreciate the value of graphs and not just look at it as another chapter in Mathematics. Who knows our lives in the future may very well hang in the balance of a graph. I thought it would be valid to put this point out for all of us to think about.
eh captain vegetable u get all these comments from ah text book
u real write boy wheyyyy
firstly the equation relating the values of voltage and current will determine the kind of graph
the graph of ph vs volume added consists of both a curve and a straight line. this is notable by the drastic decrease in ph so i will imagine for graphs that show drastic changes in its values there will be a mix of straight and curve
eh cap v slow down, slow down
the graph for a polynomial eqution with a x^3 term has turning points where the gradient equals to zero so it is possible for a graph to have more than 1 gradient
Coming back to the value of graph here is a practical example:
Have you seen the documentary An Inconvenient Truth. I am speaking of the documentary the Al Gore made to hilight the concerns and effects of global warming. I must say that throughout the presentation the graphs that he used to show the increase in temperature, CO2 levels and trends both past and present impacted me the most. The point i am trying to say is that his presentation would not have had an impact not only on myself but others without the use of graphs.
You all should have a go at the documentarry it is very informative and a good way of seeing first hand how scientists gather data and represent it on a graph.
MOOSE:
That is very true moose. So granted that it would have more than one gradient it would be useless if we could not make any deductions from this. So moose what kind of useful deductions can we make from a graph of this form.
PS MOOSE: I did not get these comments from a text book. I thought of the differnt situations that graphs of a line and a curve is applied and shared them with everyone.
in determining the axis to place each variable, how is this done when given raw data such as this
hellion i think voltage is always on the x axis....and well the current wud be on the y.....
there are basically two types of graphs... straight lines an curve .... it is quite easy to identify a straight line graph because it is usually in the form of y= mx + c...
a curve can be identify if it is raised to a power...
for instance... y=x^2..
in real life scenarios... graphs in the form of curves is quite useless and needs to be converted to a straight line and this is usually done using logs ... please correct me if i am wrong .
after watching the values its clear that its not a straight line since the values of current do not vary uniformly. It more looks like a curve. Captain vegetable!!! im reading ur comments. Im learning quite alot. dis cant possibly be a student!! Who wud spend sooo much time on this blog??? EVERYBODY I TINK ITS MISS!!! WAT U ALL TINK????
sparkle!!! u are qiute correct. I have question. Anybody know wat is the importance of the y intercept in real life applications???
what values are to be ploted on what axes??? what is the independent and dependant variables...i came across these therms while doin a log question into linear form.. please explain
To ratman:
Good sir, I don't just want to give you the solution to your question as I believe if you understand the concept it would answer most if not all concerns associated with your question so here is the concept:
1. The dependant variable depends on the value of the independant variable.
This is the underlying concept now let me explain it:
The independent variables are those that are deliberately manipulated to produce a change in the dependent variables.
eg. lets say I have two sets of variables pressure and area
In physics we know that if we decrease the area the pressure increases (in a nutshell) so if i change the value of the area and observe the change in pressure then the area acts as the independant variable (because it is the variable being changed) so the pressure is the dependant variable because the pressure DEPENDS on the area.
Having said this can you answer your question?
Excuse but captain vegetable after representing this graph how do you know these values?? I am abit lossed. Could you explain to me how do you know identify ways to simply understand these graph easily??
I must say captain vegetable you know alot. I hope to understand maths like you
i really agree with you, captain vegetable. it is true that for a straight line graph, the coordinates or points to be plotted would uniformly increase.
I WANT TO BE JUS LIKE CAPTAIN VEGETABLE WEN I GROW UP....YOURE MY HERO!!!!! ANYWAY CAPTAIN VEGETEBLE, WITH RESPECT TO UR QUESTION ON HOOKES LAW THE GRAPH WUDNT HAVE ONE GRADIANT, BUT 2 GRADIANTS. OF COURSE U WUD BE ABLE TO FIND THE GRADIANT.Y WUDNT U BE ABLE TO???? EVERYTING HAS GRADIANT!!!! RIGHT!!!!
well, captain vegetable, you must really like maths. well for the question of determinig whether you can tell when there is a curve and straight line graph, i think the points to be plotted would be the giveaway as they would not increase uniformly
Oh i 4 got!! with respect to the question on hookes law, wudnt u have to bring it to a straight line????
when a graph has both a straight line and a curve we cann use these two graphs to make comparisons at a certain point. True????
To Cruiser:
You have me confused now. Lets start over. Which graph are you reffering to?
To Cokebaby:
You talk about bringing the Hooke's Law graph to a straight line. Granted lets say we did just that. What have we accomplished by doing this?
To Cokebaby:
You talk about a 'certain point' in your comment dated ( March 5, 2008 3:53 PM) To which point are you reffering to?
To Cokebaby:
You talk about a 'certain point' in your comment dated ( March 5, 2008 3:53 PM) To which point are you reffering to?
To Cokebaby:
Please don't feel that i am interrogating you or anything of the sort. I am just trying to follow your idea on the concept.
Your comment on (March 5, 2008 3:40 PM) stated in its contents that the graph would have two gradients. Would you agree that analysis would be difficult if we were using two gradients? After all in a lab to my survey we try to make analysis using one gradient. Would you not agree?
To Dante':
I agree with what you are saying. But can this method be applied for a graph of best fit, be it a curve or straight line? In a lab when we are plotting a graph we don't get all point to line up, even if the graph is a straight line or curve.
What do you think?
Can this graph be represented to using microsoft excell
I want to try dis graph now so give me a few seconds I goin to try this
Cruiser any graph can be generated using Microsoft Excel
lIKE CAPTAIN VEGETABLE i USED mICROSOFT EXCEL TO FIND THIS AND i GOT A CURVE
this graph will give u a curve, where the graph starts at the origin. also the graph ccan give u risistance(R).
vege man how is it possible for a graph to have two gradient???????????????????????????????????????????????????
thats what i was wondering
accoding to copy cat, the graoph will give a curve, so this means that current is inversely proportional to voltage. but what i dont understand is that in the formula V = IR. V there is directly proportional to current.can someone explain this for me
this shows current against voltage and it will not give a straight line..apocalyspe i not sure if that formula applies to this but... yes v=ir and r will be wat ever number the voltage is multipiled to give the current.... but the questions jus asked wat will this give as a graph... curve or straight line??
cokebaby i think d impoetance of the y intercept is probably to show the limit. for example like captain v example with d chemical plant if the mixture is 2 high for any 1 point it can b dangerous so i think its 2 show limit. if im wrong correct me.
well the graph is a curve therefor it can hav more than 1 gradint because there is no points on the graph which when connected to form a straight line so if that is not possibe u wouldnt b able 2 find the gradient there4 u might hav 2 use limits 2 get the gradient of the curve.
thanks captian vegig 4 atempting to answer my question but i doint do physics so im kinda loss about de pressure an area example that u used...thanks any way tho.
aye i notice that the units for current is in mV. is it not supposed to be in volts? ent this will affect the outcome of the graph?
the graph will also have more than one gradient beacuse its not a straight line...and fred i think u should read again its not in mV...
captain vege i realise u does make a lot of comments... i hope u are a A+ student.... maybe u should jus get ur diploma now n go home...lol
i did plug in the values in excel and it was obviously not a straight line. :)
but i have a some what strange question... the graph is a straight line then a curve. if we need to find the gradiant when the line is still a straight line, can this be done using y2-y1 over x2-x1? or am i going wrong?
From the values seen a curve will be obtained and therefore at each point on the curve it will have a different gradient and as a result limits will have to be used
there is a curve and straight line graph, i think the points to be plotted would be the giveaway as they would not increase uniformly
Straight line graphs tend to give it away.
TO CAPTAIN VEGETABLE!!!!
I have thought long and hard about the question on Hookes Law. Since the graph comprises of a straight line and a curve, the straight line has 1 gradiant and the curve has several gradiants. Right?? But technically we dont need to find the gradiant after we exceed the straight line since the curve says that the elastic limit has been exceeded. So we dont need to find the gradiant of the curve. What is important in this experiment is the straight line. but if we look at the graph we wud c that the graph has several gradiants. OK I GOING AROUND IN CIRCLES!!!!! I MAKING ANY SENCE AT ALL?????
with respect to the question on hoookes law we do not need to bring it to a straight line. It makes no sence doing that since the curved part is of no significance!!! True?"???
i agree with coke baby in saying that graph will not produce a straight line but a curve. I figure that out by just looking at the values and then like what captain vegetablwe did i went and plotted the graph using Microsoft Excel
i believe the graph produced from the values shown would be a curve, since one of the set of values was increasing at a constant rate and the othe is increasing at a varied rate.
Using microsoft excel to porduce a graph voltage vs current you will not get a straight line but a curve.
To spartan 117
Yes you can find the gradient of the straight line using Y2-Y1/X2-x1 once the line remains a straight line.
TO FREDBURGER!!!
it really doesnt matter if ur axis is in volts or millivolts, the graph wud be the same. However if u scale the axis differently the graph wud be different.
To Cokebaby:
I agree with most of the things that you are talking about in your comments. However if i can draw refference to part of your comment where you said that the curve has no use. Is this totallly true? Doesn't the curved part gives us the behaviour of the spring after it has past the extension point?
To Cokebaby:
In addition to my last comment:
If the curve gives us the behaviour of the spring after it has exceded the extension point what can we say the role of the gradient plays in this?
To Fred Fredbuger:
Remember when we have to plot a graph after obtaining our data to go on our x and y axis we must do one of the most important part and that is calibrating our scale. So lets say that i am to plot on the y axis 10cm to 100cm. Normally a student would use 2cm (thats two small blocks) to represent 10cm. This would use 20cm on the y axis or 20 small blocks.
1. Do you agree with this scale?
2. Lets say i want to change my range data from 10cm- 100cm to
0.1m - 1m. How would I recallibrate my current scale?
TO Cruiser:
You asked how is it possible for a graph to have two gradients but doesn't a curve has multiple gradients. At each point doesn't the gradient change? Share your thoughts.
To Ratman:
I will try a different approach to explaining this concept:
lets say that I am baking bread for a baking competition.
I put the bread in the oven and start up the flame:
as the bread begins to bake it turns brown. The futher the bread bakes it turns darker brown lets call the browning of the bread bf or browning factor. Lets pretend there is such a factor on a scale of 1-10 where 1 is lightest brown then increasing in browning to 10 as being dark brown.
NOTE: If the bread remains longer in the oven the higher the (bf) would be, agree?
NOW: lets say that every 2 minutes I take a (bf) reading and after 6 minutes i get readings like this:
2(minutes) - 1 (bf)
4 (minutes) - 2 (bf)
6 (minutes) - 3 (bf)
NOW: Lets say I want to plot a graph of my results, what goes on which axis?
Well we know that there are two variables the independant variable and the dependant variable.
The independant variable is the variable that is deliberatly changed. In this instance the time is deliberately changed, I decide how long to bake the bread I decide the time. I have control over the time.
HOWEVER: the value for the (bf) depends on how long i leave the bread in the oven. If I leave the bread for another 2 minutes then the (bf) would be 4. The (bf) DEPENDS on the time. AGAIN the value of the (bf) depends on how long I leave the bread in the oven.
Therefore the (bf) is the DEPENDANT variable. Its value depends on time.
Now rule of thumb:
x axis = independant variable(time)
y axis = dependant variable (bf)
Is any of this making sense or have I burnt my bread?
To Everyone:
No one has taken the time to answer my question on March 1, 2008 2:50 PM. I really thought that this would stimulate a good discussion before the time for this blog expires.
the curve represents the ares where the elastic limit has been exceed. It shows how the spring behaves after the elastic limit has been exceeded. This curve can only be considered as being important if u want to study the behaviour of the curve after the elastic limit has been exceeded. one important point to note however is the point at which the the spring loses its elasticy. This is the point at which the line turns into a curve. Normally when experiments are conducted on hookes law we normally study the straight line and not the curve...not that the curve is of no significane.its just that the straight line obeys hokkes law!!!!
to captain vegetable:
you are absolutely correct that the grqaph is not a straight line; I did the graph using MS excel and obtained an exponential curve of the current in mA curve and A relatively straight line for the voltage. Unfortunately I am unable to bring it into the blog.
first u have to plot the points in excel then u have to log the two, voltage and the current to get a straght line, so a gradent can de found and other calculations may be encounted.
yes a straight line and a curve in one graph can be possible, any u can tell hou it is going to look in a graph (eg)of such a graph is:
x= 2,4,6,8,10,14,22,29,37.
y= 5,10,15,20,27,34,41,53.
the straight line part is:
x= 2,4,6,8,10
y= 5,10,15,20
why? because all the points are evenly apart, how can u tell, gust by finding the difference to any two x or y vlue to the answer will be the same.
note that the difference of the x values will be the same and the y value will be the same.
and the curve part is:
x= 14,22,29,37.
y= 27,34,41,53.
U will have to do the same as above to dertermine if the difference is common if not then the values is not equal and it is a curve.
TO CAPTAIN VEGETABLE!!!!
With respect to your question dated March 1, 2008 2:50 PM..the two chemicals are mixed proportionally. This represents a straight line. when the line curves... this says dat the substances are not mixing proportionally. This cud mean dat the rate of mixing has slowed. The rate at which the chemicals are added remains the same, but the rate at which they mix slows down....I TINK!!!!
if i were the operator...a change in the shape of the graph wud not be a gud sign. I wud have to bring the graph back to a straight line. The problem lies in the mixing so i might have to change the ratio of the chemicals added. am i on the right track?????
i tink i have the wrong idea for this question. Ideas anyone????
Anyone know to get this graph back to a straight line?????
To captain vegetable:
with the question concerning the industrial plant and the two units A and B as a mixture; i think that the sudden change in the graph from a straight line to a curve would indicate that there was a change in the rate of mixing btw A and B which was not constant but fluctuating at different points...i think this should be of some concern because this could affect the end product...since there would be in turn a reactant in excess as one of the units is used up before the other. From the graph you may determine which of the units is in excess and to correct this error, if internal, u must increase the input of the limiting unit or the unit that was used up first...but Cveggie how come u ent put any comment for the 1/2mv^2 post...
to captain vegetable:
dated in march,3,2008 at exactly 2:50pm, u posted a comment.
1. if i was the operator, and i saw this change., i would say that the rate of A decreased while the rate of B remained constant.
2. YES. this is important! VERY!
a sligt change in the rate of flow of the chemicals could change thestructure of the product: for instance, in the Harbour process (manufacturing ammonia) the workers have to supply nitrogen and hydrogen at a certain proportion( i.e. 1:3) to produce nitrogen.
if they used differerent proportions of these chemicals, they could get contaminated ammonia( ammonia with excess N2 or H2)
3.what could be done is to lower the rate of flow of B or adjust the rate of A to its standard proportion.
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