Question

A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The energy dissipated gets doubled if

• A. both the length and the radius of the wire are halved
• B. both the length and the radius of the wire are doubled
• C. the radius of the wire are doubled
• D. the length of the wire are doubled

Answer 1

The correct option is B both the length and the radius of the wire are doubled

Energy dissipated in wire is given by

$E=\frac{V^2}{R}\Delta t$,

Where, $R=\frac{\rho l}{A}$

For constant voltage,

$E\propto \frac{1}{R}\propto \frac{A}{\rho l}$

For same material

$E\propto \frac{r^2}{l}$

So, if both the length and the radius of the wire are doubled, the energy dissipated gets doubled.

Hence, option $\left(b\right)$ is correct.