• # 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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