Question: Joule's Law of heating.

[vaishnavsm]

Hi!

My text says that when the resistance is doubled, the heating effect is halved.
Joule's law of heating states that Resistance is Directly proportional to Heat produced.
I.E, R α H.
∴ 2R α 2H.
So, shouldn't the Heat be doubled.

Or, since the Potential Difference is constant, should I use
H = (V² t) / R
instead of
H = I²Rt
?
Does Joule's law apply everywhere, or are there conditions?
Just to be clear, this isn't homework.
Thanks!
Vaishnav

 

[darkxponent]

Hi!

My text says that when the resistance is doubled, the heating effect is halved.
Joule's law of heating states that Resistance is Directly proportional to Heat produced.
I.E, R α H.
∴ 2R α 2H.
So, shouldn't the Heat be doubled.

Or, since the Potential Difference is constant, should I use
H = (V² t) / R
instead of
H = I²Rt
?
Does Joule's law apply everywhere, or are there conditions?
Just to be clear, this isn't homework.
Thanks!
Vaishnav

You can use both equations as both are same. Putting V = IR in first gives the second equation.

When resistance doubled, what happens to the current through the resisrance?

 

[darkxponent]

R α H.

NOT always. It is applicable to a certain condition, that is?

 

[CWatters]

My text says that when the resistance is doubled, the heating effect is halved.

Correct. That follows from..

Power = V²/R .... (1)

Joule's law of heating states that Resistance is Directly proportional to Heat produced.

Joules law states that the heat produced in a conductor by a constant current is equal to the product of the square of the current and resistance of the conductor and the duration of time the current passes. eg.. Q = I² * R * T

So

Power = Q/T
So

Power = I² * R .....(2)

It may appear that (1) and (2) are contradict each other but that's wrong. As darkxponent points out, if you change R you change I. That's because in a simple resistor circuit I is not independent of R...

From Ohms Law..

I = V/R

Substutute for I in (2) gives

Power = (V/R)² * R

= V² /R

Which is equation (1)

 

[vaishnavsm]

Thank YOU!

Thank You Guys!
I knew that you can replace V = IR to get the equation.
I didn't know joule's law stated constant current as a requirement.
Thanks SO Much!

Best Regards,
Vaishnav.

[CLOSED]

 

[darkxponent]

Thank You Guys!
I knew that you can replace V = IR to get the equation.
I didn't know joule's law stated constant current as a requirement.
Thanks SO Much!

Best Regards,
Vaishnav.

[CLOSED]

Would like to add a bit more to the thread. The basic power equation is VI, derived from Electromagnetics, so Joules Law is not a 'Law' at all. This, P=VI, equation is valid everywhere, even when I varies non-linearly with V(where impedance is not constant).

Consider a case where where I = k*V^2.
In this case Power equation will become. p = k*V^3