Question

According to Joules law, if the potential difference across a conductor of resistivity $\rho$ remains constant, then the heat produced is proportional to:

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

Answer 1

Answer: (A)

$\frac{1}{\rho }$

$\text{Joule's law}$

When a constant e.m.f. is applied to a conductor , the heat produced is Q

1) $Q\propto i^2$, the square of the current passing through it.

2) $Q\propto R$, the resistance of the conductor .

3) $Q\propto t$ the time flow of the current .

hence according to joule's law

$Q=i^{2}rt$

now, $i=\frac{v}{r}$

$\therefore$ $Q=\frac{v^2}{r}t$

since potential difference is constant.

$Q\propto \frac{1}{r}$ and $r\propto \rho$

$Q\propto \frac{1}{\rho }$