How to conserve energy with electrical noise? If a resistor experiences thermal noise, it will dissipate energy to the environment. But where does the resistor's energy come from? It seems that it will just lose energy until ran out. 
 A: It works just like every other kind of thermal energy. If a resistor can give out energy to the environment, it can also receive it. For example, if it gives it out by radiating, it can also absorb radiation; if it gives it out by having its fast-moving atoms smash into air molecules, then fast-moving air molecules can also smash into it. When it's in thermal equilibrium with its environment, it'll give out energy at the same rate it receives it.
A: It "runs out" when it reaches thermal equilibrium with it's environment. In that case, as @Kevin points out, the dissipation equals the absorption from the environment. If you pass a current through the resistor, it will heat up and that will drive extra current/voltage noise in the resistor. FYI: Resistive cooling of ions in a Penning trap uses a cooled resistor to dissipate the ion energy via mirror currents. If the resistor was not cooled, then the thermal noise in the resistor would heat the ions to room temperature, i.e. into equilibrium with the resistor's temperature.
A: resistor is an electric component which is used for the purpose to restrict the electron flow. if you run with 10Km/hour speed now i will stop you is it possible to stop you suddenly. No it is not possible. so that resistor dissipate some energy in the form of heat. 
