• question_answer
                    A \[{{5}^{\text{o}}}C\] rise in temperature is observed in a conductor by passing a current. When the current is doubled the rise in temperature will be approximately:                                                            

    A)                 \[{{16}^{\text{o}}}C\]

    B)                 \[{{10}^{\text{o}}}C\]

    C)                 \[{{20}^{\text{o}}}C\]

    D)                 \[{{12}^{\text{o}}}C\]

    Correct Answer: C

    Solution :

                    Key Idea: When current is passed through a conductor, electric energy is absorbed by the conductor through collisions between its atomic lattice and the charge carriers causing its temperature to rise.                 Energy loss in conductor \[Q={{i}^{2}}RT\]                 Heat developed \[=ms\,\Delta \theta \] \[\therefore ms\,\Delta \theta ={{i}^{2}}Rt\] or            \[\Delta \theta \,\propto \,\,{{i}^{2}}\]                 \[\frac{\Delta {{\theta }_{2}}}{\Delta {{\theta }_{1}}}=\frac{i_{2}^{2}}{i_{1}^{2}}\]                 or            \[\Delta {{\theta }_{2}}={{\left( \frac{{{i}_{2}}}{{{i}_{1}}} \right)}^{2}}\,\Delta {{\theta }_{1}}\]                 Here \[{{i}_{2}}=2{{i}_{1}},\,\,\Delta {{\theta }_{1}}={{5}^{o}}C\]                 From Eq. (i)                 \[\therefore \Delta {{\theta }_{2}}={{\left( \frac{2{{i}_{1}}}{{{i}_{1}}} \right)}^{2}}\times 5\]                 \[=4\times 5={{20}^{o}}C\]

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