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Power Dissipation, Joule's Law...

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aryajur

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I have a basic confusion. Suppose an electronic circuit is connected to a battery of voltage V and is drawing a current I, we say that it is consuming power

P=V.I

But looking at Joule's Law which states the power dissipated is given as:

P=∫E.Jdv

Now if the conductor is of uniform cross section then dv = dA dl and

P=∫E dl . ∫J ds = VI

So why is it that we take power dissipation always the product of voltage and the current without bothering about the type of conductor???
 

Becoz the current factor takes type of conductor into account.

i.e. curret flowing in all conductors is not same.

if you recall the expression for current (or current density) it also depends on drift velocity which I think explains your doubt.
 

It is clear that P=VI doesn't hold every where . in fact it is an approximated ralationship of P=∫EJ .
 

I think billano is right, because when we consider electronic circuits, which are driven by a battery, then the battery sees the whole circuit as an equivalent resistance connected by 2 wires. The current that is drawn from the battery is the only current being drawn. So we can replace J.S in the Joule's law equation with the current and which is a constant irrespective of the position of this equivalent circuit. So it can be taken out of the integral. Next no matter how we go from the positive to the negative terminal in the integral
∫E dl
we will always get the potential difference as V. So for electronic circuits we will always have power P=VI irrespective of the shape of conductors in the circuit.[/b]
 

When you calculate the value of resistance, you take specific resistence which is characteristic of a material. So we never spare it's influence.

Regards
drdolittle :)
 

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