Maybe you are in a lab with a kit of resistors. Somebody was kind enough to put the kit together, but the technical references for the resistors aren't readily available. The maker of the kit knows the power ratings, but it's after hours, and he's not available.
I remember that in the first practicum of the introductory EE course we were instructed to "sacrifice" a quarter-watt resistor to see and smell how components burn. The instructor would tell us matter-of-factly: "dial your power supply to 12V, take a 10Ω resistor, now connect the resistor to power supply with alligator clips." It was a surprise for most students that the resistor immediately burned and smoked.
How much power will the resistor have to dissipate?P = I2 R = V2 / R, where R is the value of your resistor. Figure out a way to estimate the current through the resistor, or voltage across it. Resistance is known. Calculate power.
(To be more exact, it's VRMS or IRMS. If the voltage and current approach DC, then the RMS value approaches the DC value.)
Attempt to look-up the power ratings. Avoid guesswork if you can.Even though this write-up is about educated guessing; guesswork should be last resort, not first. Make an effort to find ratings provided by the curator of the kit or the supplier of resistors. The raring may be written somewhere on the kit. If the part number of the resistor is known, then you can look up the power rating in the datasheet.
How to make an educated guess about the power rating.
The larger the mechanical size of the resistor, the more power it can dissipate, the greater the power rating is. So, it is possible to estimate the power rating of common** throughole based on outside dimensions. Measure the length and diameter and look-up the power rating in the table.
|Power rating||Body length, l||Body diameter, d|
|watts||inch [mm]||inch [mm]|
|0.125 (1/8)||0.130 ± 0.012 [3.30 ± 0.30]||0.067 ± 0.012 [1.70 ± 0.30]|
|0.25 (1/4)||0.236 ± 0.012 [6.00 ± 0.30]||0.091 ± 0.012 [2.30 ± 0.30]|
|0.5 (1/2)||0.335 ± 0.039 [8.50 ± 1.00]||0.106 ± 0.020 [2.70 ± 0.50]|
These dimensions come from the resistors' datasheets. Since these axial throughole resistors are standardized, the datasheets from different manufacturers agree with each-other.
** Note, we are talking only about "garden variety" throughole resistors like the ones in the photo above. We are not talking about power resistors like this or this.
What if you don't have the resistor with the required power rating on hand?1/4-watt is the most common size of a resistor that you will come across in hacker spaces, practicum labs in schools, and such. 1/4-watt is more than enough for small-signal circuits. What if you calculations show that you need to dissipate more than 1/4 watt? You have several options:
- Procure a beefier resistor
- Connect multiple resistors in series or parallel, such that their effective resistance has the desired value. The combined power which they can dissipate will be equal to the sum of their power ratings.
- Change your circuit to lower the power that the resistor would have to dissipate (perhaps temporarily until you procure a resistor with a sufficient power rating).
References Datasheets for the "garden variety" axial throughole resistors: Stackpole Electronics, Philips, Panasonic, generic Chinese. The datasheets agree with each-other, despite different manufacturers. Common MIL standards were driving the design of resistors for a long time.
 Resistor Sizes and Packages