A) \[9{}^\circ C\]
B) \[18{}^\circ C\]
C) \[27{}^\circ C\]
D) \[36{}^\circ C\]
Correct Answer: B
Solution :
From Joules law of heating, the heat developed is equal to \[H={{I}^{2}}RT\] ... (i) Amount of heat used in raising the temperature \[=mc\Delta T\] ... (iii) Heat developed in conductor = Heat used in raising the temperature \[\therefore \] \[{{I}^{2}}R\,t=mc\Delta T\] \[\Rightarrow \] \[\Delta T\propto {{I}^{2}}\] \[\therefore \] \[\frac{\Delta {{T}_{1}}}{\Delta {{T}_{2}}}={{\left( \frac{{{I}_{1}}}{{{I}_{2}}} \right)}^{2}}\] \[={{\left( \frac{I}{3I} \right)}^{2}}=\frac{1}{9}\] \[\Rightarrow \] \[\Delta {{T}_{2}}=9\Delta {{T}_{1}}=9\times 2={{18}^{o}}C\]
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