• # question_answer Two resistances ${{R}_{1}}$ and ${{R}_{2}}$ when connected in series and parallel with 120 V line, power consumed will be 25 W and 100 W respectively. Then the ratio of power consumed by ${{R}_{1}}$ to that consumed by ${{R}_{2}}$ will be                       [EAMCET 1983] A)            1 : 1                                           B)            1 : 2 C)            2 : 1                                           D)            1 : 4

$P=\frac{{{V}^{2}}}{R}$Þ $\frac{{{P}_{P}}}{{{P}_{S}}}=\frac{{{R}_{S}}}{{{R}_{P}}}=\frac{({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}/({{R}_{1}}+{{R}_{2}})}=\frac{{{({{R}_{1}}+{{R}_{2}})}^{2}}}{{{R}_{1}}\,{{R}_{2}}}$ Þ $\frac{100}{25}=\frac{{{({{R}_{1}}+{{R}_{2}})}^{2}}}{{{R}_{1}}{{R}_{2}}}$ Þ $\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{1}$