Question

A constant voltage is applied between the two ends of a metallic wire. Some heat is developed in it. The heat developed is 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 is halved
• D. the length of the wire is doubled

Answer 1

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

$Q=\frac{V^2}{R}$
But $R=\frac{pl}{\pi r^2}$
Therefore $Q=\left(\frac{\pi V^2}{p}\right)\frac{r^2}{1}$
Q is doubled if both l and r are doubled