Question

According to Joule's law, if 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:

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

Answer 1

The correct option is D $\frac{1}{\rho }$

Heat $=\frac{V^2}{Rt}$

Heat $=\frac{V^{2}A}{\rho Lt}$

As area, length, potential difference remains constant for the conductor and time is not changed, hence
Heat $\propto \frac{1}{\rho }$