Electronic – Using multiple current sense resistors in parallel to handle a high current measurement with cheaper resistors

The 1 W resistor will get less hot that the 1/4 W resistor if they both dissipate the same power. The specific heat may be comparable, but because of the higher mass the 1 W resistor will need more power to get the same temperature rise.

You may need to place several resistors in series to prevent overheating. suppose you have a 1 kΩ/ 1/4 W resistor which has 20 V across it. Then the power will be (20 V)\$^2\$/ 1 kΩ = 400 mW, which is more than the 1/4 W the resistor is rated for, and which will reduce the resistor's life. You can use a 1 W version instead or for instance three 330 Ω/ 1/4 W resistors in series. Each will then dissipate only 130 mW, so that's a safe value.

Note that resistors can only dissipate their rated power at low temperatures. Most must be derated above 70 °C environment temperature, which means that the higher you go beyond that temperature the less power it may dissipate, until its maximum temperature, where the allowed dissipation becomes zero.

Apart from spreading power you also may need a couple of series resistors for high voltage applications. A resistor may be rated at 160 V, then you can't use it for 230 V, even if the current (and thus power) are very low. 230 V AC is 325 V peak, so you'll need 3 resistors in series.

Seems like you want to get the max power from the resistors and power supplies that you've got. 3D printing is a long process. I don't see how temporarily exceeding the rated power dissipation can help. The following is for the steady state.

12x 1Ω resistors, each rated for 10W. The max steady state overall power you can dissipate is 120W. Each resistor dissipates \$P = I^2R\$. The max rated power is reached when

\$I=\sqrt{\dfrac {P_{rated}} R}=3.16A \approx 3A \$

Pick a series/parallel combination of resistors such that

\$\dfrac {V_{supply}} {R_{series}} \approx 3A\$ (just under 3A)

This can be achieved by using the 12V power supply and resistors in 3x parallel strings each with 4x resistors in series. Each string will pull 3A. Together, all 3x strings will pull 9A. The 12V power supply in the O.P. is rated for 18A. It should be able to supply the current.

Construction tips

• Use thermal grease
• Thermally insulate the bottom of the plate, if possible.