Graphs with multiple equations

[plzNOCarribbean]

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So I have been having trouble analyzing graphs (probably because of my weak math background) but I stumbled upon this thanks to Bloodysurgeon and it helped but I have a few questions:

If A is proportional to B think straight line slope

If A is proportional to B^2 think of an upward curved slope (like a half-U but starting from A=0, B=0)

If A is proportional to 1/B think downward curve approaching but never touching 0

If A is proportional to B^1/2 think "r" shaped curve (as if there were an asymptote at y=x but there isn't).

^when it says A is proportional to B^1/2, is that the same as A is proportional to the square root of B?

Also, what about deciding relationships for concepts with multiple equations. For instance, I know P=IV but there is also P=(I^2)(R). So for the graph, would we have power on the y axis and current on the x axis and see a linear graph where P is proportional to I or would we see an exponential graph where P is proportional to I^2? How do you know which is right??
I've seen a lot of these equations for one concept like the PE stored in capacitors which is why I wanna get this before my test. Thanks guys! 😀

 

[plzNOCarribbean]

sorry, and one other thing to add that I forgot to mention

in regards to: If A is proportional to 1/B think downward curve approaching but never touching 0.
^is this the same as saying two variables are inversely proportional to eachother? am I correct in thinking that this is the kind of graph we see when we look at current and resistance when rearranging ohms law to V/R=I?

so, would the Resistance be on the X-axis and Current on the Y-axis? and we would see a downward slope? This would show that current decreases as the resistance increases?

OR

am I completely wrong and do we need voltage on the y axis and resistance on the x-axis based on the way I rearranged ohms law above. Since slope =rise/run= dy/dx is the slope equal to current?

Sorry, I know this was an extremely long post I apologize but again I really appreciate the clarification from anyone because I've been struggling with graph problems and I think it's because of a lack of really knowing whats going on.

 

[Rabolisk]

when it says A is proportional to B^1/2, is that the same as A is proportional to the square root of B?

Yes.

Also, what about deciding relationships for concepts with multiple equations. For instance, I know P=IV but there is also P=(I^2)(R). So for the graph, would we have power on the y axis and current on the x axis and see a linear graph where P is proportional to I or would we see an exponential graph where P is proportional to I^2? How do you know which is right??

They're both right. They are just two different cases.

in regards to: If A is proportional to 1/B think downward curve approaching but never touching 0.
^is this the same as saying two variables are inversely proportional to eachother? am I correct in thinking that this is the kind of graph we see when we look at current and resistance when rearranging ohms law to V/R=I?

so, would the Resistance be on the X-axis and Current on the Y-axis? and we would see a downward slope? This would show that current decreases as the resistance increases?

OR

am I completely wrong and do we need voltage on the y axis and resistance on the x-axis based on the way I rearranged ohms law above. Since slope =rise/run= dy/dx is the slope equal to current?

Again, they are both right. You can choose what goes on the y axis and what goes on the x axis. The important thing is that you can relate between an equation and a graph. The best way to do that is to put the variable on the y axis on one side and everything else on the other side. Depending on what the equation looks like (e.g. y = x, y = 1/x, y = x^2, etc.). Note that when you are comparing two variables, which is what graphs on R2 are intended to do, you must keep everything else constant.

 

[plzNOCarribbean]

Rabolisk, thank you for clarifying! makes much more sense but, what do you mean by "they are both right. they are just different cases"

isn't it that by double current you get double the power, or by doubling the current your power increases by a factor of 4. I don't get how the relationship can just change between these two variables and not be one definitive case all of the time.

 

[Rabolisk]

Power isn't only dependent on current. I can double the current through a resistor, but that doesn't mean that power will double or quadruple necessarily. The equations tell you what the other conditions must be for simple relationships to hold.

 

[ThirdEye]

P=IV and V=IR

Replacing V with IR (since they are equal) into P=IV ----> P = I(IR) = (I^2)R


If you double the current, power increases by a factor of 4 in BOTH cases.

In P = IV when you double I you also have to double V since V = IR.

 

[Rabolisk]

In P = IV when you double I you also have to double V since V = IR.

Why?