# What is the relation between the power dissipation in resistor and the temperature rise

Which relation we use to calculate the temperature rise in resistor using the power dissipation. If we take P=R*I^2 from resistor, how much the resistor heats in this case ? I know that in transsitor the relation between the power dissipation and the temperature is given by: Pd = (Tj-Ta)/theta(ja), I try to find the relation of the resistor dissipation but i didn't find anything helpful! Thank you for your help.

• Can we use the Stefan-Boltzmann Law, if we suppose that the thermal energy is transferred by radiation ? Dec 10, 2014 at 8:43
• It depends on the Resistor. Think about: Casing, Airflow, Heatsink, outside temperature. Look at datasheets: Datasheets. There you will have the power dissipation rating. Dec 10, 2014 at 9:22
• If you want to calculate it, then you need to define the geometry(I suggest a cube) and calculate the heat dissipation coefficients for the surfaces. Then you need to find the thermal equilibrium, to get the final temperature(where dissipation=power input). Dec 10, 2014 at 9:24
• The datasheets give you the rating power dissipation and not the applied power (it's depend on the current flow the resistor) Dec 10, 2014 at 9:25
• They give you the maximum power that can be dissipated without a heatsink in a standard environment(at room temperature, standard air pressure and so on). So yes, they don't give it. Dec 10, 2014 at 9:27

The relationship in both cases is Temperature Rise = Power * thermal resistance.

• Tj-Ta is the temperature rise (from "junction" to "ambient)
• theta(ja) is the thermal resistance. And the assumption is that the data sheet gives you this value.

This relation works just like E=IR only it's temperature and heat instead of voltage and current. The relationship you gave for the transistor is in a less useful form for this purpose. You want to apply a little algebra and thus come up with:

Tj-Ta = Pd * theta(ja)

This works for resistors as well, assuming the data sheet will give you a theta value from the resistor body to air. That's the equivalent of junction-to-ambient. In all but high-power pulse operation, it's just assumed that the resistor transfers all of the dissipated power to its body, and you only worry about how it transfers to the surrounding air.

Actually, in the real world, both the resistor and the transistor can transfer a considerable amount of heat out through its leads (or pads). Since your stated equation only mentions junction-to-ambient, that's all that's addressed here.

If you can't get a theta value, you'd have to come up with an allowable maximum temperature for the resistor, and use the resistor's stated power rating to arrive at a value for theta.