Question

When a constant voltage is applied between the ends of a metal wire. Heat produced in this wire will be 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 doubled.
• 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

Here, the heat produced, $H=\frac{V^2}{R}t$
Resistance , $R=\frac{\rho l}{\pi r^2}$
so, $H=\frac{\pi r^{2}V}{\rho l}t$
if $l\to 2l,r\to 2r,H\to \frac{\pi 4r^{2}V}{\rho 2l}t=2H$