Q: Why, after ironing, is the live pin of my 13-amp plug hot while the neutral pin is not? Surely the same amount of current flows through both.
A: The live pin is warmer than the neutral because of the fuse in the plug. The thinner conductor inside the fuse is designed to melt if excessive current flows through it. Therefore it runs hotter than the connecting wires for normal loads, which has the additional effect of warming the live pin by conduction.
A: The live pin is warmer because the plug or the socket is faulty. I recommend that it be replaced as soon as possible to avoid any risk of fire. Heat is caused because the live pin is not making adequate contact in the socket and there is a resistance that is generating heat. There is no faulty contact on the neutral pin.
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The effect of the heat will be to increase the corrosion on the pin, which will increase the heat generation and so on until the plug/socket combination catches fire, or preferably blows the fuse or trip. This could occur if corrosion products build up to the point where a live/earth or live/neutral connection is made.