Two heating coils one made of thin wire and the other of thick wire, same material, same length are connected one by one to the same source. which coil will produce more heat? justify

Heat in a form of magnetic field energy can be calculated using: where L is induction: and I electric current. The number of wraps N around coil is conditioned by the length of coil and thickness of wire. The more thick the wire the less wraps of wire around the coil while length will not change anything because it is the same. So if you make less wraps around the coil and construct the formula: and simplify it to: which would mean that when your wire is thinner you produce more heat because you can make more wraps around the coil.

Hope this helps.

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