1. Car relay wire gauge

I have a SPST relay with terminals 30, 85, 86 and 87 that I want to use to feed 12V switched power to the carputer according to the following image:

If I understand this correctly the current from terminal 86 to terminal 85 is only used for powering the relay itself. Can you please confirm that it is safe to use a 0.75mm2 (18 AWG) wire on 86 and 85, and a 6mm2 (10 AWG) wire on 30 and 87 to feed 12V switched power to the PSU (15A fused).

2. The Coil should be fine with an 18AWG wire. It pulls very little power and could easily use smaller wire.

The power feed wire will need to be sized accordingly to the power of your PSU and the length of the wire you are running. You can always check by using a volt meter. Check how much voltage drop there is from the beginning of the wire to the end.

In practice if you are under 10' and around 100 watts or under then your 10AWG wire will likely be big enough. If you are unsure then use an 8AWG wire. Too big a wire is not an issue but too small a wire is.

You can check voltage drop with a volt meter and it is simple to do. You hook the ground of the meter to a common ground point. Make sure your meter can reach both ends of the wire without moving your ground location. You then place the positive of your meter to the beginning of the wire and then at the end. Your difference should be very minimal if anything. Try it again with the computer powered up and the voltage drop should be the same otherwise the wire is too small. You should run this test both with the computer on and off with the vehicle in the same position. Running or not. The actual drop will be the voltage at the end of the wire compared to the beginning of the wire. The end of the wire should always be less than the front if not the same.

3. if you can measure or know your max current for the PSU input(supply), you can calculate your voltage drop with this calculation;
voltage drop calculator
total voltage drop must not exceed %5.

4. Thanks for the tip regarding measurement of the voltage drop, I will test this. The wire is around 8' and the PSU is fused at 15A. I believe a 10 AWG wire should handle 15A, but just to be on the safe side I will use a 10A fuse near the battery. The system itself only draws ~6A anyway (the PSU is somewhat overdimensioned to avoid any thermal stress).

My main question was regarding the relay to make sure that the terminals 85 and 86 was used only for the coil so that 18 AWG was sufficient. I got an answer for this so now I can continue with my build

5. test it before you actually hook it to the computer though if you are not sure. Most 12 volt relays I have seen have a diagram on the relay on how the internals are laid out. I don't recall what the terminal numbers are off the top of my head but the container should say or they are common enough they should be the same.

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