Question

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

• A. Both the length and radius of the wire are halved
• B. Both the length and 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 radius of the wire are doubled

Heat developed in circuit is $H=\frac{V^2}{R}$
We know that:

$R=\frac{\rho L}{A}=\frac{\rho L}{\pi r^2}$ where $\rho =$ resistivity, $L=$ length of wire and $A=\pi r^2$, cross sectional area of wire.
Thus, $H=\frac{V^2\pi r^2}{\rho L}$
So, $H\propto \frac{1}{L},H\propto r^2$
Thus when length and radius is doubled, heat is doubled.