Power dissipation question I^2 R

[bonbon22]

Homework Statement

Why is the graph of power dissipated against current a parabolic shape?

https://filestore.aqa.org.uk/sample-papers-and-mark-schemes/2018/june/AQA-74072-QP-JUN18.PDF


question 28 in the multiple choice section near the bottom of the pdf

Relevant Equations

P = I * V
P = I ^2 R

I understand that when using the equation I^2 * R that current is meant to be constant in each component? I got the idea from this video

So how can we use this equation to find the relationship between varying current against power? As the current is at a constant?...

 

[phinds]

Problem Statement: Why is the graph of power dissipated against current a parabolic shape?
P = I ^2 R

Uh, when you plot P=(I^2)R what do you think you SHOULD get?

 

[bonbon22]

Uh, when you plot P=(I^2)R what do you think you SHOULD get?

if i have the equation p =current * voltage here the current is proportional to the power ? not to the current ^2

 

[phinds]

if i have the equation p =current * voltage here the current is proportional to the power ? not to the current ^2

You need to re-read the question

 

[bonbon22]

You need to re-read the question

let me rephrase it then...
why is power dissipated = current ^2 * resistance and not Power times Current ... ?

 

[phinds]

let me rephrase it then...
why is power dissipated = current ^2 * resistance and not Power times Current ... ?

Relevant Equations: P = I * V

 

[bonbon22]

i don't get what your saying m8
is power proportional to current
or is power proportional to current squared ?

 

[jbriggs444]

P = I * V is all well and good. On the surface, that looks like power (P) should be proportional to current (I). But that only works as long as you do not look closely at V and simply pretend that it is a constant.

V = I * R

In the situation at hand, you should be holding R constant, systematically varying I, measuring the resulting P and letting V be whatever it needs to be.

 

[PeroK]

i don't get what your saying m8
is power proportional to current
or is power proportional to current squared ?

To add to the above: when there are many variables, you can't simply say $A$ is proportional to $B$, as it may depend on what else is held constant.

$P = IV = I^2R$

is actually as good an example of this as any.

Another example is the acceleration for uniform circular motion:

$a = \omega v = \omega^2 r$

 

[jbriggs444]

$a = \omega v = \omega^2 r$

One of my favorites is the $r$ dependency in $a=\frac{4 \pi^2 r}{t^2} = \frac{v^2}{r}$

 

[CWatters]

Sorry if this is obvious but just in case you are struggling with the differences...

I understand that when using the equation I^2 * R that current is meant to be constant in each component? I got the idea from this video

In the video the resistors are connected to a constant voltage so the current flowing is indeed constant.

The problem statement says..

Which graph shows how power dissipated P varies with current I in a component that obeys ohm's law?

So here the words "varies with current" means the current is an input variable. If you were doing the lab experiment you would be changing the current somehow and measuring the power.

If the component obeys ohm's law like a resistor then varying the current also varies the voltage, so in the equation..

P=IV

Both I and V would be changing because V is a function of I.

If you double I then V also doubles and the power goes up four times.