Q110 / 180 · AIIMS 2015 · Physics
When a current is passed in a conductor, $5^{\circ} \mathrm{C}$ rise in temperature is observed. If the strength of current is made thrice, rise in temperature will be
- A$5^{\circ} \mathrm{C}$
- B$20^{\circ} \mathrm{C}$
- Correct answerC$45^{\circ} \mathrm{C}$
- D$15^{\circ} \mathrm{C}$
Solution
Joule heating in a wire, $H=I^2 R t$
For given $R$ and $t, H \propto I^2$
$$
\therefore \frac{H_1}{H_2}=\frac{I_1^2}{I_2^2}
$$
Also, $H=m s \Delta T$
For given $m$ and $s, H \propto \Delta T$
$$
\therefore \frac{H_1}{H_2}=\frac{\Delta T_1}{\Delta T_2}
$$
For eqn. (i) and (ii)
$$
\frac{I_1^2}{I_2^2}=\frac{\Delta T_1}{\Delta T_2}
$$
Here, $I_1=I, \Delta T_1=5^{\circ} \mathrm{C}, I_2=3 I$
$$
\begin{aligned}
& \Delta T_2=? \\
& \therefore\left(\frac{I}{3 I}\right)^2=\frac{5}{\Delta T_2} \text { or } \Delta T_2=45^{\circ} \mathrm{C}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.