Question

A wire made of a material with a resistivity $\rho$ has a radius $r$ and is a length $L$, then a certain voltage $V$ is placed across it.
Which of the following are directly proportional to the power being dissipated?

• A. $L$
• B. $L$ and $\rho$
• C. $L,V,$ and $\rho$
• D. None of the above

Answer 1

The correct option is D None of the above

Cross-section area of the wire $A=\pi r^2$

Thus resistance of the wire $R=\rho \frac{L}{A}=\rho \frac{L}{\pi r^2}$

$\therefore$ Power dissipated $P=\frac{V^2}{R}=\frac{V^2\left(\pi r^2\right)}{\rho L}$

$⟹$ $P\propto V^2{r}^2$

Thus option D is correct.