A) \[{{5}^{\circ }}C\]
B) \[{{10}^{\circ }}C\]
C) \[{{20}^{\circ }}C\]
D) \[{{40}^{\circ }}C\]
Correct Answer: C
Solution :
Key Idea: Electrical energy is converted into heat energy. From Joule?s law, for a current carrying conductor at definite temperature the rate of production of heat is directly proportional to the square of current \[\left( {{i}^{2}} \right)\] between, then \[H={{i}^{2}}\,RT\] Where \[R\] is resistance and \[t\] is time. Also heat required to raise the temperature is \[H=mc\,\Delta \,\theta \] We have \[mc\,\Delta \,\theta ={{i}^{2}}\,R\,t\] \[\Rightarrow \] \[\Delta \,\theta \,\propto {{i}^{2}}\] \[\left( \frac{\Delta \,{{\theta }_{1}}}{\Delta \,{{\theta }_{2}}} \right)=\frac{i_{1}^{2}}{i_{2}^{2}}\] \[={{\left( \frac{{{i}_{1}}}{2{{i}_{1}}} \right)}^{2}}=\frac{1}{4}\] \[\Rightarrow \] \[\Delta \,{{\theta }_{2}}=4\times \Delta {{\theta }_{1}}=4\times 5={{20}^{\circ }}C\]
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