Q. Two wires A & B of the same material and length , have their cross-sectional area in the ratio - 1:4. What should be the ratio of heat produced in these wires, if the voltage applied is the same across?

A/C to Joule's law of heating;

H = I² Rt = V² t / R

So, voltage remaining same for two wires, the heat produced is inversely proportional to the resistance of the wire.

Now, R = ? l/a

Therefore, H = V² t / (? l/a) = V² at / ? l

Hence, Heat produced in wire A / heat produced in wire B = 1/4