What is the apparent difference between the two cases of H=I^2RT and H=(V^2)T/R?

[shihab-kol]

Homework Statement

H=I^2RT and H=(V^2)T/R.
In one case H is directly proportional to R while in the other it is not where H is the energy consumed.
Explain the apparent difference between the two cases

Homework Equations

None

The Attempt at a Solution

In the first case electricity is being converted to heat while in the second electric energy is being obtained from something else.So the equations are different
My version is you can derive the two equations from one another

Thus they are same
But it's this alright?

 

[haruspex]

In the first case electricity is being converted to heat while in the second electric energy is being obtained from something else.

No, they describe the same circumstance.
Consider the other difference in the equations. One has V where the other has I.
What happens to these when the resistance changes?

 

[shihab-kol]

No, they describe the same circumstance.
Consider the other difference in the equations. One has V where the other has I.
What happens to these when the resistance changes?

Ok
So for getting V we have to include it
So is my edited post correct?(post 1)

 

[haruspex]

Ok
So for getting V we have to include it
So is my edited post correct?(post 1)

No, as I thought I had indicated, it is completely wrong. The two equations apply to the same circumstance. What you need to explain is why they are consistent, despite appearances.
Try to answer my question in post #2.

 

[shihab-kol]

I has to decrease and V increase if we increase R and vice versa
What I meant by my previous post was that you could derive both formulas from one another .For including V we have to include the inverse of R, thus both equations mean the same thing.
So,is it alright?

 

[haruspex]

What I meant by my previous post was that you could derive both formulas from one another .For including V we have to include the inverse of R, thus both equations mean the same thing.

Yes, but I don't feel it gets to grips with the apparent paradox.

I has to decrease and V increase if we increase R and vice versa

Sort of.
P=V²/R seems to say that if you increase R P decreases. What assumption is being made in saying that?
P=I²R seems to say that if you i ncrease R P increases. What assumption is being made in that case?

 

[shihab-kol]

P=V^2 /R says what you say .But if we increase R then V and so V^2 has to increase
Thus,P has a change
P=I^2R means as R increases I^2 has to decrease balancing the equation and more or less making it equal to the first one.
So,is this it?
P.S.- These are due to Ohm's Law

 

[haruspex]

But if we increase R then V and so V^2 has to increase

as R increases I^2 has to decrease

Not necessarily.
You don't seem to be grasping the question. The question is saying "if we look at the equation P=V²/R then we might expect that if R increases then P decreases". Do you agree with that statement? What assumption is being made in making that statement?

 

[shihab-kol]

Not necessarily.
You don't seem to be grasping the question. The question is saying "if we look at the equation P=V²/R then we might expect that if R increases then P decreases". Do you agree with that statement? What assumption is being made in making that statement?

We are saying that P is inversely proportional to R.
In decreasing R we have to increase I and I is directly proportional to P {P=VI} .
So, yes I think P will increase.

 

[haruspex]

In decreasing R we have to increase I

To deduce that you must make a certain assumption. What assumption is being made?

 

[shihab-kol]

To deduce that you must make a certain assumption. What assumption is being made?

That voltage is constant.

 

[haruspex]

That voltage is constant.

Right!
Now look at the other equation, P=I²R. This appears to say that if R decreases P decreases. What assumption is being made now?

 

[shihab-kol]

Right!
Now look at the other equation, P=I²R. This appears to say that if R decreases P decreases. What assumption is being made now?

That current is constant

 

[haruspex]

That current is constant

Right. So how would you answer the question now? What explains the apparent paradox?

 

[shihab-kol]

Sorry for the delay.

Is it that in same time,t since both V and I are constant R is also a constant?

 

[haruspex]

Sorry for the delay.

Is it that in same time,t since both V and I are constant R is also a constant?

No. Forget I, V and R for the moment and think in these general terms:
We have two equations, both valid.
If we make a certain assumption in one we reach a certain conclusion.
If we make a different assumption in the other, we reach a contradictory conclusion.
What can we say about the two assumptions?

 

[shihab-kol]

No. Forget I, V and R for the moment and think in these general terms:
We have two equations, both valid.
If we make a certain assumption in one we reach a certain conclusion.
If we make a different assumption in the other, we reach a contradictory conclusion.
What can we say about the two assumptions?

That anyone assumption is wrong?

 

[haruspex]

That anyone assumption is wrong?

Not exactly. I think it will take forever to get there this way, so I shall just tell you how I would answer:
The two assumptions cannot be true at the same time. So it should not be surprising that the two assumptions lead to contradictory conclusions.