Why does resistive heating equal the electrical power P=RI²?

[quasar987]

Griffith's saying that in a resistor, P = RI² is the rate at which heat is dissipated. Is that suposed to be intelligible to someone who has no knowledge in thermodynamics?

Can someone explain this process to me. What is HEAT? And how does the rate at which work is being done by the electrostatic force on the electrons in the resistor a measure in all point equal to that of the rate at which heat is dissipated?

 

[jamesrc]

Heat is a form of energy (measurable in Joules). The effects of electrical resistors in a circuit are analogous to friction in a mechanical system: energy is "lost." In either case, the energy is converted to thermal energy (thus, "heat is dissipated"). The effect in question is known as Joule heating: the temperature of the resistor rises as current is passed through it. That's how my toaster works anyway. I hope that helps. If my reply is too simplistic, I'm sure someone else will provide some better help soon.

 

[Gokul43201]

Does it help to observe that $\Delta W = q \Delta V$, that [tex]P = dW/dt [/itex], and that the drift velocity of an electron at a certain point in a circuit is a function of only the properties of the conductor at that point ?<br /> <br /> A more intuitive approach might be to observe that electrons transfer momentum to the lattice through collisions, raising the vibrational energy of the atoms (ions) that they collide with. This large local lattice energy dissipates itself conductively through the wire (phonon modes) or through radiation.[/tex]