• # 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

$\frac{H}{t}=P=\frac{{{V}^{2}}}{R}\Rightarrow P\propto \frac{1}{R}$ 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 $\frac{{{P}_{A}}}{{{P}_{B}}}=\frac{l_{B}^{2}}{l_{A}^{2}}=\frac{4}{1}\Rightarrow {{P}_{A}}=20\,W$