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

  • question_answer  Two wires A and B of same material and mass have their lengths in the ratio 1 : 2. On connecting them to the same source, the rate of heat dissipation in B is found to be 5W. The rate of heat dissipation in A is [AMU (Engg.) 2000]

    A)            10W                                         

    B)            5W

    C)            20W                                         

    D)            None of these

    Correct Answer: C

    Solution :

                       \[\frac{H}{t}=P=\frac{{{V}^{2}}}{R}\Rightarrow P\propto \frac{1}{R}\] also \[R\propto \frac{l}{A}\propto \frac{{{l}^{2}}\rho }{A.l\rho }\]                    Þ \[R\propto \frac{{{l}^{2}}}{m}\] Þ \[R\propto {{l}^{2}}\] (for same mass)            So \[\frac{{{P}_{A}}}{{{P}_{B}}}=\frac{l_{B}^{2}}{l_{A}^{2}}=\frac{4}{1}\Rightarrow {{P}_{A}}=20\,W\]

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