Q123 / 125 · BITSAT 2015 · Physics
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
- Aboth the length and the radius of the wire are halved.
- Correct answerBboth the length and the radius of the wire are doubled.
- Cthe radius of the wire is doubled.
- Dthe length of the wire is doubled.
Solution
The heat produced is given by
$$
H=\frac{V^{2}}{R} \text { and } R=\frac{\rho \ell}{\pi r^{2}}
$$
$\therefore H=V^{2}\left(\frac{\pi r^{2}}{\rho \ell}\right)$
or $\quad H=\left(\frac{\pi V^{2}}{\rho}\right) \frac{r^{2}}{\ell}$
Thus heat $(H)$ is doubled if both length $(\ell)$ and radius $(r)$ are doubled.
Hence, the correct answer is option: 'B'.