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

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In summary, the conversation discusses the relationship between power, resistance, voltage, and current in a circuit. The two equations, P=IR^2 and P=ΔV^2/R, seem to be in conflict as one states that power increases with resistance while the other states that a decrease in resistance increases power. However, it is clarified that both equations assume that all other factors are constant. When voltage is constant, increasing resistance increases power, but when current is constant, increasing resistance decreases power. The concept of maximum power transfer is also mentioned. Overall, the conversation highlights the importance of considering all factors and variables when analyzing the relationship between power and resistance in a circuit.
  • #1
Perseverence
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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
 

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  • #2
Perseverence said:
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?
 
  • #3
the information I am trying to glean is the effect of increasing resistance on power when all other factors are constant.
 
  • #4
Perseverence said:
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.
 
  • #5
Perseverence said:
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?
 
  • #6
cnh1995 said:
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.
 
  • #7
Please refer to the attached image for clarification.
 
  • #8
Yes, it is Delta V squared. My apologies. V stands for VOLTAGE
 
  • #9
haruspex said:
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.:smile:
Perseverence said:
V stands for VOLTAGE
Right, but voltage "across" what? Can you derive one formula from the other?
 
  • #10
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
 
  • #11
Perseverence said:
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?
 
  • #12
cnh1995 said:
What is the effect of increasing resistance on the current through the resistance?
... if voltage is constant.
 
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  • #13
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.
 
  • #14
Thanks ! This was my first pos to this forum and you guys were great :)
 
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  • #15
Perseverence said:
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.
 
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  • #16
cnh1995 said:
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.
cnh1995 said:
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
 
  • #17
Perseverence said:
Makes sense. Thank you
No probs!
And welcome to PF!:smile:
 
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  • #18
Perseverence said:
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.
 
  • #19
haruspex said:
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.
 
  • #20
Perseverence said:
Yes, I understand what you were saying now.
Thank you. Your statement helps me understand this concept a lot more
 

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

1. What is the difference between P = IR^2 and P=delta v/r?

In P = IR^2, P represents the power in an electrical circuit, I represents the current, and R represents the resistance. This formula is used to calculate the power dissipated in a resistor. On the other hand, P = delta v/r represents the power in a mechanical system, where delta v is the change in velocity and r is the radius of the circular path. This formula is used to calculate the power required to keep an object moving in a circular path.

2. Can these two formulas be used interchangeably?

No, these formulas cannot be used interchangeably. P = IR^2 is specific to electrical circuits, while P=delta v/r is specific to mechanical systems. They have different variables and applications.

3. How do these formulas relate to each other?

Both formulas involve the concept of power, which is the rate at which energy is transferred or work is done. In P = IR^2, power is related to the electrical energy dissipated in a resistor, while in P=delta v/r, power is related to the work done to maintain an object's circular motion.

4. What is the significance of the "P" in both formulas?

The "P" in both formulas represents power, which is an important concept in science and engineering. It helps us understand how energy is being transferred or used in a system.

5. Can these formulas be used to solve real-world problems?

Yes, these formulas can be used to solve real-world problems. For example, P = IR^2 can be used to calculate the power dissipated in a light bulb, while P=delta v/r can be used to calculate the power required to keep a car moving in a circular track. These formulas are commonly used in various fields, such as electrical engineering and mechanics, to solve practical problems.

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