• # question_answer Resistances ${{R}_{1}}$ and ${{R}_{2}}$ are joined in parallel and a current is passed so that the amount of heat liberated is ${{H}_{1}}$ and ${{H}_{2}}$ respectively. The ratio $\frac{{{H}_{1}}}{{{H}_{2}}}$ has the value [MP PMT 1994] A)            $\frac{{{R}_{2}}}{{{R}_{1}}}$                                            B)            $\frac{{{R}_{1}}}{{{R}_{2}}}$ C)            $\frac{R_{1}^{2}}{R_{2}^{2}}$                                        D)            $\frac{R_{2}^{2}}{R_{1}^{2}}$

Heat produced $H=\frac{{{V}^{2}}t}{4.2R}=H\propto \frac{1}{R}$ Hence $\frac{{{H}_{1}}}{{{H}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}$