Question

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

• A. $\rho$
• B. $\rho^{2}$
• C. $\frac{1}{\sqrt{\rho}}$
• D. $\frac{1}{\rho}$

Answer 1

Answer: (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 $P \propto \frac{1}{\rho}$.