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Yes, because a thinner wire has higher resistance and dissipates more energy as heat.

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Q: If you were to use two different gauge sizes of wire per leg of a three phase electricity installation would the smaller gauge wire of the parallel set get hotter than the larger size wire of that set?

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voltage gets smaller

In parallel.

If you need a resistor of a certain value, and you have no resistors with small enough values,you can create the one you need by connecting several of those you have in parallel.The effective net resistance of resistors in parallel is always less than the smallest individual.And the more resistors you add in parallel, the smaller the net effective resistance becomes.

A thin (smaller diameter) wire resist more electricity than a thick (larger diameter) wire. Just like a larger pipe will allow more water to flow than a smaller pipe, a larger wire has more cross-sectional area to allow more current to flow.

Call the total effective resistance 'R'. If the values of the individual parallel resistors are 'A', 'B', 'C', 'D' etc., then 1/R = (1/A) + (1/B) + (1/C) + (1/D) etc. Or, R = 1 divided by { (1/A) + (1/B) + (1/C) + (1/D) } The more resistors there are in parallel, the SMALLER the effective resistance becomes.

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voltage gets smaller

voltage gets smaller

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they were smaller

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