JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors Question Bank Heating Effect of Current

  • question_answer Two wires 'A' and 'B' of the same material have their lengths in the ratio 1 : 2 and radii in the ratio 2 : 1. The two wires are connected in parallel across a battery. The ratio of the heat produced in ?A? to the heat produced in ?B? for the same time is                                                                     [MNR 1998]

    A) \[1:2\]                                     

    B) \[2:1\]

    C) \[1:8\]                                     

    D)  \[8:1\]

    Correct Answer: D

    Solution :

    \[{{R}_{1}}=\rho \frac{{{l}_{1}}}{{{A}_{1}}}\] and \[{{R}_{2}}=\rho \frac{{{l}_{2}}}{{{A}_{2}}}\]Þ \[\,\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}.\frac{{{A}_{2}}}{{{A}_{1}}}=\frac{{{l}_{1}}}{{{l}_{2}}}{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]                    Given \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{1}{2}\] and \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{2}{1}\] or \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{2}\]Þ \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{8}\]            \[\therefore \] Ratio of heats \[\frac{{{H}_{1}}}{{{H}_{2}}}=\frac{{{V}^{2}}/{{R}_{1}}}{{{V}^{2}}/{{R}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{8}{1}\]

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