Heater cartridge with 7.2 ohms - 12 or 24 V?

I have a heater cartridge here that measures 7.2 Ω.

• At 12 V that would amount to 20 W
• At 24 V that would amount to 80 W

The cartridge itself is 2 cm long

Could it handle both voltages or is this clearly an under-powered 12 V cartridge?

• Just give it 15V, what controller board are you using? – Perplexed Dipole May 15 '19 at 13:49
• The question is what voltage, and/or continuous power level, is the cartridge rated for? You're going to dump roughly the same total energy to reach a given temperature setpoint regardless of input voltage. ("Roughly" because there is heat loss from the hotend to air) – Carl Witthoft May 15 '19 at 14:32
• any way I can figure that out? – matthias_buehlmann May 15 '19 at 15:04
• The same total energy given a set temperature, but a higher wattage will have a higher max temp and be able to heat up quicker. Regardless I don't see how we can determine the rated voltage with the information provided. We would be better off looking at the source of the heater cartridge, from a pre assembled printer, printer kit, preassembled hotend, or sourced individually. If it was sourced with the rest of the printer what voltage of the PSU? – Perplexed Dipole May 15 '19 at 15:09
• @user1282931 as my answer explains, you might need to supply photos - both possible types exist. – Trish May 15 '19 at 16:24

e3D Heater Cartridges are documented to be around 4.8 Ω for 12 V & 30 W, 3.6 Ω for 12 V & 40 W, 19.2 Ω for 24 V 30 W and 14.4 Ω for 24 V 40 W.

7.2 Ω is a value quite far away from these values - about double of what the 12 V versions are listed and about a third/half of a 24 V heater cartridge. So it is not a cartridge that is similar to those. I have contacted e3D about updating the specs of their High Precision Heater Cartridges to include the nominal resistances to get more references, but that information is pending.

However, we don't need that. A variant of Ohm's law can help us estimate what this cartridge could be: Power is the square of Voltage (U) divided by Resistance.

$$P=\frac {U^2} R = \frac {144\ \text V^2}{7.2\ \Omega} = 20\ \text W$$

$$P=\frac {U^2} R = \frac {576\ \text V^2}{7.2\ \Omega} = 80\ \text W$$

Mounted in a 12 V Machine this should act work at 20 W, in a 24 V it would work at 80 W. It does not say, however, if it is designed to get powered with 12 V or 24 V. It doesn't help, that both types exist: I was able to find 12 V 20 W heater cartridges just as well as 24 V 80 W heater cartridges. If it is an underpowered 20 W one and mounted in a 24 V machine, you risk burning it though, but not the other way round.

To differentiate what exactly you have, a photo of the heater cartridge would be needed - it should bear at least a marking of what it's nominal wattage or voltage is.