Conflict in formulas P = IR^2 and P=delta v/r

[Perseverence]

P = IR^2 and P=delta v/r

Did the first equation is Joules heating law, which shows that power increases with resistance. The 2nd equation which is given as an answer in my problem set states that a decrease in resistance increases power. The inconsistency is really bothering me. Help please

 

[haruspex]

P = IR^2 and P=delta v/r

Did the first equation is Joules heating law, which shows that power increases with resistance. The 2nd equation which is given as an answer in my problem set states that a decrease in resistance increases power. The inconsistency is really bothering me. Help please

It depends what is being held constant.
In I²R, increasing resistance will increase power assuming current is constant.
What assumption does the other equation make? Can both these assumptions be true at once?

 

[Perseverence]

the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.

 

[haruspex]

the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.

So try to answer the questions I posed.

 

[cnh1995]

the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.

Can you get the relation P=I²R from P=ΔV²/R?
What does ΔV stand for here?

 

[haruspex]

Can you get the relation P=I²R from P=ΔV²/R?
What does ΔV stand for here?

Yes, I was just about to point out that P=ΔV/R makes no sense. It should of course be V²/R.

 

[Perseverence]

Please refer to the attached image for clarification.

 

[Perseverence]

Yes, it is Delta V squared. My apologies. V stands for VOLTAGE

 

[cnh1995]

Yes, I was just about to point out that P=ΔV/R makes no sense. It should of course be V²/R.

Actually, I was referring to the attached image. Yes, the OP made a typo, but my question was to see if the OP can relate the two formulae.

V stands for VOLTAGE

Right, but voltage "across" what? Can you derive one formula from the other?

 

[Perseverence]

Both of the equations assume that all other factors are constant. One is essentially Ohm's law. Given that all other factors are constant what would be the effect of increasing resistance on power

 

[cnh1995]

Both of the equations assume that all other factors are constant. One is essentially Ohm's law. Given that all other factors are constant what would be the effect of increasing resistance on power

What is the effect of increasing resistance on the current through the resistance?

 

[haruspex]

What is the effect of increasing resistance on the current through the resistance?

... if voltage is constant.

 

[Perseverence]

Ah, okay. I see it you can derive one equation from the other. They do seem at first to be in conflict. But it does still seem to be somewhat contradictory that in one instance resistance is directly proportional power and in the other it is inversely proportional.

It's still twists my brain a bit. I guess the rule is that when all other factors are constant decreasing resistance increases power.

 

[Perseverence]

Thanks ! This was my first pos to this forum and you guys were great :)

 

[cnh1995]

It's still twists my brain a bit. I guess the rule is that when all other factors are constant decreasing resistance increases power.

That is true if the voltage across the resistance remains constant i.e. in case of a circuit containing parallel resistances connected across a voltage source.

If you have a series circuit containing two resistors r and R in series with a constant voltage source, and you are changing R keeping all the other parameters constant, you can't make the above statement about the power dissipated in R. Look up 'maximum power transfer' theorem.

 

[Perseverence]

That is true if the voltage across the resistance remains constant i.e. in case of a circuit containing parallel resistances connected across a voltage source.

If you have a series circuit containing two resistors r and R in series with a constant voltage source, and you are changing R keeping all the other parameters constant, you can't make the above statement about the power dissipated in R. Look up 'maximum power transfer' theorem.

That is true if the voltage across the resistance remains constant i.e. in case of a circuit containing parallel resistances connected across a voltage source.

If you have a series circuit containing two resistors r and R in series with a constant voltage source, and you are changing R keeping all the other parameters constant, you can't make the above statement about the power dissipated in R. Look up 'maximum power transfer' theorem.

Makes sense. Thank you

 

[cnh1995]

Makes sense. Thank you

No probs!
And welcome to PF!

 

[haruspex]

I guess the rule is that when all other factors are constant decreasing resistance increases power.

No, this is why I asked the questions I asked. You cannot hold all else constant. With voltage constant, increasing resistance reduces current and power; with current constant (by some means) increasing resistance increases voltage and power.

 

[Perseverence]

No, this is why I asked the questions I asked. You cannot hold all else constant. With voltage constant, increasing resistance reduces current and power; with current constant (by some means) increasing resistance increases voltage and power.

Yes, I understand what you were saying now.

 

[Perseverence]

Yes, I understand what you were saying now.

Thank you. Your statement helps me understand this concept a lot more