# Thread: Heat dissipation in a resistor

1. I have been facing a problem related to electricity since quite a long time. The topic is heating effect of electric current.
My textbook says that the electrical energy is used up in useful work such as rotating the blades of a fan, etc in an electrical circuit. But when we consider a purely resistive circuit, consisting of a battery and a resistor, the entire electrical energy gets dissipated as heat through the resistor.

Then there is the derivation of the formula, that when a charge Q flows across a resistor across which the voltage is V, then the work done by the cell to move the charge will be VQ.
Let I be the current in the circuit and t be the time through which the charge Q flows across the resistor.
Then the power of the cell will be P = W / t
P = VQ / t ....... P = VI
The energy supplied by the cell will be E = P x t
And this energy is dissipated as heat it is written....
Therefore, H = VIt

Q 1) what is meant the electrical energy? The kinetic energy of the electrons??
Q2) How EXACTLY does this electrical energy get converted into heat energy in a resistor? why does this change even occur?

What happens to the charges inside the resistor, for why does the cell has to expend its energy to keep the charges flowing through the resistor ? Related question,
Why does this heating not occur in a conducting wire?

Please explain the phenomenon according to the math used....
Thank you so much 

2. Originally Posted by Gaurav(-26.7)
I have been facing a problem related to electricity since quite a long time. The topic is heating effect of electric current.
My textbook says that the electrical energy is used up in useful work such as rotating the blades of a fan, etc in an electrical circuit. But when we consider a purely resistive circuit, consisting of a battery and a resistor, the entire electrical energy gets dissipated as heat through the resistor.

Then there is the derivation of the formula, that when a charge Q flows across a resistor across which the voltage is V, then the work done by the cell to move the charge will be VQ.
Minor quibble, but potentially important for answering your question properly: The work is not necessarily done by the cell (e.g., signs matter). But the work done on the charge will be the VQ product you gave.

Let I be the current in the circuit and t be the time through which the charge Q flows across the resistor.
Then the power of the cell will be P = W / t
Another minor quibble: It would be better to express P as the time derivative of work.

P = VQ / t ....... P = VI
The energy supplied by the cell will be E = P x t
And quibble again: E would be the time-integral of power.

And this energy is dissipated as heat it is written....
Therefore, H = VIt

Q 1) what is meant the electrical energy? The kinetic energy of the electrons??
In general what is meant by "electrical energy" is actually "the energy supplied by (or to) the electric field." That energy may or may not equal the kinetic energy of the electrons -- many processes may carry off (or supply) energy. For example, if I heat the resistor enough, it will glow. So the energy supplied to the resistor will not be entirely accounted for by the kinetic energy of the electrons. In fact, the lowly incandescent lamp rather depends on the kinetic energy not being equal to the energy supplied.

Q2) How EXACTLY does this electrical energy get converted into heat energy in a resistor? why does this change even occur?
There are several abstractions one may use to provide an explanation. The word "EXACTLY" is troublesome.

In a classical picture (originally published by Drude), inelastic collisions of electrons with the fixed atoms of a resistive material cause the latter to heat up. Think about a crowd of humans trying to traverse a narrow passageway. They will bump into each other, exchanging energy in the process.

Drude's model also provided the first rigorous derivation of Ohm's law, explaining why the "law" did not always hold. The law, such as it is, posits a linear relationship between the voltage across a conductor, and the current through it. The constant of proportionality was given the name resistance:

V = IR.

What happens to the charges inside the resistor, for why does the cell has to expend its energy to keep the charges flowing through the resistor ?
The same inelastic collisions invoked above explain why energy must be continuously supplied. Once the energy supply stops, so does the net motion of the charge carriers. (There is still random, Brownian, motion, but no net transfer of energy occurs in such a case.)

Related question,
Why does this heating not occur in a conducting wire?
I don't know why you think that. Except for superconductors, all conductors are resistive and thus dissipate energy.

Please explain the phenomenon according to the math used....
Thank you so much 
Just include Ohm's law in your equations and you will be able to derive an expression for the power consumed by a resistor, entirely in terms of any two of (voltage, current and resistance).

3. Thanks tk421.....that helped a lot👍

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