Question

According to Joule's law, if the potential difference across a conductor of resistivity $\rho$ remains constant, then the heat produced in the conductor is proprotional to

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

Answer 1

Answer: (A)

$\frac{1}{\rho }$

We know,
$P=\frac{V^2}{R}$
but,
$R=\frac{\rho L}{A}$
$P=\frac{V^2}{\frac{\rho L}{A}}$
$P=\frac{A{V}^2}{\rho L}$
$P\propto \frac{1}{\rho }$ ........$($since $\frac{A{V}^2}{L}=$ constant$)$