• # question_answer 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                                     [MP PMT 1986] A)            $\rho$                                  B)            ${{\rho }^{2}}$ C)            $\frac{1}{\sqrt{\rho }}$  D)            $\frac{1}{\rho }$

$P=\frac{{{V}^{2}}}{R}$ but $R=\frac{\rho l}{A}$ Þ $P=\frac{{{V}^{2}}}{\rho l/A}=\frac{A{{V}^{2}}}{\rho l}$. Since $\frac{A{{V}^{2}}}{l}$is constant as per given conditions So $P\propto \frac{1}{\rho }.$