Question

A constant voltage is applied on a uniform wire, then the heat is produced. The heat so produced will be doubled, if

• A. The length and the radius of wire are halved
• B. Both length and radius are doubled
• C. Only the length is doubled
• D. Only the radius is doubled

Answer 1

Answer: (B)

Both length and radius are doubled

Answer 2

By using $H = \frac{V^{2}t}{R}$ and $R = \rho\frac{l}{A} = \frac{\rho l}{\pi r^{2}}$ ⇒ $H = \frac{V^{2}t\pi r^{2}}{\rho l} \Rightarrow H \propto \frac{r^{2}}{l};$ on doubling both r and l heat will be doubled.