A) \[9{}^\circ C\]
B) \[18{}^\circ C\]
C) \[27{}^\circ C\]
D) \[36{}^\circ C\]
Correct Answer: B
Solution :
The heat developed in conductor due to current \[={{i}^{2}}Rt\] ...(1) Amount of heat energy used in raising temperature of the wire\[=mc\text{ }\Delta T\] ...(2) Since, the heat developed in the conductor is used in raising the temperature of the comductor so, \[{{i}^{2}}Rt=mc\Delta T\] \[\Rightarrow \] \[\Delta T\propto {{i}^{2}}\] \[\therefore \] \[\frac{\Delta {{T}_{1}}}{\Delta {{T}_{2}}}={{\left( \frac{{{i}_{1}}}{{{i}_{2}}} \right)}^{2}}={{\left( \frac{i}{3i} \right)}^{2}}\] \[=\frac{1}{9}\] \[\Rightarrow \] \[\Delta {{T}_{2}}=9\Delta {{T}_{1}}\] \[=9\times 2\] \[=18{}^\circ C\]
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