According to Joule's law, if the potential difference across a conductor having a material of specific resistance remains constant, then the heat produced in the conductor is directly proportional to
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(d) $P = \frac{{{V^2}}}{R}$ but $R = \frac{{\rho l}}{A}$ $ \Rightarrow $ $P = \frac{{{V^2}}}{{\rho l/A}} = \frac{{A{V^2}}}{{\rho l}}$. Since $\frac{{A{V^2}}}{l}$is constant as per given conditions So $P \propto \frac{1}{\rho }$.
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