According to Joule's law, if the potential difference across a conductor having a material of specific resistance $\rho$ remains constant, then the heat produced in the conductor is directly proportional to

Let the specific resistance of the material be ρ.

∴  Resistance of the conductor  is given by     R=​$\frac{\rho L}{A}$

We know that power P=$\frac{V^2}{R}$​

According to Joule's law of heating, the heat produced in time t is given by,

    H=P×t=$\frac{V^{2}t}{R}$

∴   H = $\frac{V^{2}At}{\rho L}$         

⟹H ∝ ​$\frac{1}{\rho }$