The heat produced by electric current is directly proportional to the resistance.Now the heater element has very high resistance so a lot of heat is produced in the heater element due to which it becomes very hot and glow.On the other hand,the cord of an elecric heater has very low resistance due to which very little heat is produced in it and so the cord becomes slightly warm but doesn 't glow.
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Joule's law of heating
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The resistance of cord is usually of copper and aluminium which is very low so, it doesn't glow.
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