# Why do we have to compute maximum safe current through resistor equalizing heat exerted by the resistor and heat created in resistor?

My book says says resistance of a wire = $\rho l/\pi r^2$ where $\rho$= resistivity of the resistor material. l=length of the resistor. R= radius of the resistor so heat produced H = $I^2 \rho l$/ $J \pi r^2$ J= joule constant. Then heat to exerted by the resistor per second us $2\pi rlh$ if h= heat exerted by the unit area of the resistor per unit second. So by equalizing both we get maximum current as $I_{max}^2$ = 2 $\pi^2 J h r^3/ \rho$. So my question is why do we equalize those heats?

## 1 Answer

When current passes through a resistor, heat is generated and initially its temperature increases. As its temperature increases from its surroundings, it starts to dissipate the heat, and the rate of dissipation of heat is proportional to the difference between the temperature of the two (when this difference is small. See Newton's law of cooling).

As the temperature of the resistance increases, after a certain time, it has enough temperature so that the rate of creation of heat is same as the rate of dissipation, and the temperature of the resistor does not increase anymore, it reaches an equilibrium.

In the calculations you have provided, we assume that this equilibrium has been achieved, and thus, the rate of generation of heat is the same as that of dissipation.