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)

$\frac{1}{\rho}$

Answer 2

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