Physics - Current Electricity Question with Solution | TestHub

Joule heating in a wire, $H=I^{2}Rt$ For given $R$ and $t,H\propto I^2$ $$\therefore \frac{H_1}{H_2}=\frac{I_1^2}{I_2^2}$$ Also, $H=ms\Delta T$ 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, $I_1=I,\Delta T_1=5^{\circ }\mathrm{C},I_2=3I$ $$\begin{array}{rl}& \Delta T_2=?\\ & \therefore {\left(\frac{I}{3I}\right)}^2=\frac{5}{\Delta T_2}\text{ or }\Delta T_2=45^{\circ }\mathrm{C}\end{array}$$