Question

According to Joules' law, if the 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 $\frac{1}{\rho }$

Let the specific resistance of the material be $\rho$.

$\therefore$ Resistance of the conductor is given by $R=\rho \frac{L}{A}$

We know that power $P=\frac{V^2}{R}$

According to Joule's law of heating, heat produced in time $t$ is given by,

$H=P\times t=\frac{V^{2}t}{R}$

$\therefore$ $H=\frac{V^{2}t}{\rho L/A}=\frac{V^{2}At}{L}\frac{1}{\rho }$

$⟹H\propto \frac{1}{\rho }$

Answer is D.