Thermal Resistance

Thermal resistance, written R_θ, is the thermal-domain analogue of electrical resistance. It quantifies how many kelvins of temperature rise occur per watt of heat flowing through a given path: ΔT = P × R_θ. A resistor's body-to-ambient thermal resistance (R_θ_BA) determines how hot it gets in service — a 100 W RH-100 with R_θ_BA = 1.3 K/W on a heatsink runs at 130 K above ambient at full power; without the heatsink R_θ_BA jumps to 4 K/W and the same 100 W produces 400 K rise — well past the safe limit.

The path from element hot-spot to ambient is typically a series of resistances: element-to-case (R_θ_EC, controlled by the potting compound), case-to-heatsink (R_θ_CH, controlled by the thermal interface material and torque), and heatsink-to-ambient (R_θ_HA, set by sink size and airflow). Adding them yields the total. For SMD chip resistors the path is element → solder pad → PCB copper → ambient air, with R_θ_BA typically 100 – 300 K/W for an 0805 part.

Thermal resistance is the key number for system thermal design. Specifying a 50 % derating without checking R_θ in the actual mounting can result in field failures when the apparently-conservative resistor still cooks. Datasheets publish R_θ for several mounting scenarios; designers should measure or simulate (FEA, Spice thermal) for non-standard mountings.