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TWO HEATER MADE UP OF SAME MATERIAL ARE CONNECTED ACROSS IN PARALLEL ACROSS THE MAINS.THE LENGTH AND DIAMETER OF THE WIRE OF ONE OF THE COIL ARE DOUBLE THAN THE OTHER WHICH ONE OF THEM WILL PRODUCE MORE HEAT AND WHY?

therefore

 

Here same material is used.So resistivity constant for both coils.

A = ?r²

For the coil with length L and diameter d,the resistance  R = 4L/( ?d^{2  )}

For the coil with length 2L and diameter 2d,the resistance  R = 2L/( ?d^{2  )}

We know that the resistance increases,heat produced will also increases.So the first coil produce more heat.