Question

When a current is passed in a conductor, 5 ${}^{\circ }$C rise in temperature is observed. If the strength of current is made thrice, rise in temperature will be

• A. 5 ${}^{\circ }$C
• B. 20 ${}^{\circ }$C
• C. 45 ${}^{\circ }$C
• D. 15 ${}^{\circ }$C

Answer 1

Answer: (C)

Joule heating in a wire,
H = I² R t
For given R and t, $H\infty I^2$
$\therefore \frac{H_1}{H_2}\frac{I_1^2}{I_2^2}\dots \left(i\right)$
Also, $H=ms\Delta T$
For given m and s, $H\infty \Delta T$
$\therefore \frac{H_1}{H_2}=\frac{\Delta T_1}{\Delta T_2}\dots \left(ii\right)$
For eqn. $\left(i\right)$ and $\left(ii\right)$
$\frac{I_1^2}{I_2^2}=\frac{\Delta T_1}{\Delta T_2}$
Here,$I_1=I,\Delta T_1=5^{\circ }C,I_2=3I$
$\Delta T_2=?$
$\therefore {\left(\frac{I}{3I}\right)}^2=\frac{5}{\Delta T_2}$Or $\Delta T_2=45^{\circ }C$