Question

A constant voltage is applied between the two ends of a uniform metallic wire. It generates some heat, when the heat output will double. proof mathematically​

Answer 1

The heat developed is doubled if. Heat developed will be doubled when R is halved. Further, R=ρl/(πr2)andH=V2πr2t/ρl. So heat produced when both the length and radius of the wire are doubled.

Answer 2

Explanation:

joules heating law startes H=I²RT

since V is constant the current won't change, the resistance of the wire will not change either since it's on uniform composition so the heat output will only be doubled if the temperature becomes twice of the present degree.

other factors to alter the heat will be:

1) To change the material of the wire of and making it of a material of higher resistivity

2) increasing the length of the wire

3) reducing the area/radius of the wire

4) increasing the voltage and current in the circuit