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I have a 40W ceramic heater, which needs to work with 24V but I only have a 12V power supply.

Will the heater work with 12V?

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Yes, but it'll only use a quarter of the power (10 watts) and put out a quarter of the heat.

Per Ohm's law, V=IR, with half the voltage, I'll draw half the current. Per P=IV, with half voltage and half current, it'll consume one quarter power.

Note that this is approximate since, as @Brian Drummond pointed out, the resistance of the heater may be lower when cooler. This will increase the power at lower voltage, but only slightly.

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    \$\begingroup\$ It may be slightly more powerful than 10W as its heating element won't reach the same temperature, thus working at a slightly lower resistance, consuming slightly more than half the current, but this is probably close enough. \$\endgroup\$ – Brian Drummond Oct 7 '15 at 16:05
  • \$\begingroup\$ @Brian Drummond: If it's nichrome wire, its resistance doesn't change significantly with temperature. That's one of the reasons nichrome is used in heaters. \$\endgroup\$ – Fizz Oct 7 '15 at 16:09
  • \$\begingroup\$ @RespawnedFluff - A ceramic heater doesn't use nichrome wire, does it? en.wikipedia.org/wiki/Heating_element#Ceramic_heating_elements \$\endgroup\$ – scanny Oct 7 '15 at 19:55
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    \$\begingroup\$ That article is one of the most confused on Wikipedia (if you read all of it--never mind the tags), so who knows... Around my back of the woods, often enough the nichrome wire is incorporated in a factory-made sealed "ceramic" disc element (actually something made of aluminium borosilicate, IIRC) and you can't see any wire except two short leads. I wouldn't bet most people can tell this apart from a PTC ceramic by just looking... including the OP. And, yeah I did tear one apart so I'm sure mine had nichrome wire inside. YMMV. \$\endgroup\$ – Fizz Oct 7 '15 at 20:13
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You might as well use or build a DC-DC boost converter to double the voltage for your heater. David Jones explains it in details on his video blog.

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    \$\begingroup\$ A 40W boost converter is probably out of the realm of someone asking this question. \$\endgroup\$ – Matt Young Oct 7 '15 at 16:04
  • \$\begingroup\$ I never make assumptions of this kind. If the OP feels confident enough at least he hast the information. What he does [or not] with it is up to him. \$\endgroup\$ – user59864 Oct 7 '15 at 16:12

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