Question

A constant voltage is applied between the ends of a wire. The heat developed is doubled, if

• A. both length and radius are halved
• B. both length and radius are doubled
• C. only the radius is doubled
• D. only the length is doubled

Answer 1

Answer: (B)

both length and radius are doubled

$Heat\propto \frac{V^2}{R};R=\frac{\rho L}{A}$

$Heat\propto \frac{A{V}^2}{\rho L}$

for heat to double $\frac{A}{L}$ should double

So, $\frac{r^2}{L}$ should double.