Question

the resistance of to resistors in parallel combination is 2ohm and in series combination 9ohm .the two resistors are

Answer 1

$$\begin{gathered} \mathbf{Resistors}\mathbf{}\mathbf{in}\mathbf{}\mathbf{series}\mathbf{:} \\ {\mathrm{R}}_{\mathrm{se}}={\mathrm{R}}_1+{\mathrm{R}}_2 \\ \mathrm{So}, \\ {\mathrm{R}}_1+{\mathrm{R}}_2=9......\left(1\right) \\ \mathbf{Resistors}\mathbf{}\mathbf{in}\mathbf{}\mathbf{parallel}\mathbf{:} \\ {\mathrm{R}}_{\mathrm{pa}}=\frac{{\mathrm{R}}_1{\mathrm{R}}_2}{{\mathrm{R}}_1+{\mathrm{R}}_2} \\ \mathrm{So}, \\ 2=\frac{{\mathrm{R}}_1{\mathrm{R}}_2}{9} \\ {\mathrm{R}}_1{\mathrm{R}}_2=18......\left(2\right) \\ {\left({\mathrm{R}}_1-{\mathrm{R}}_2\right)}^2={\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)}^2-4{\mathrm{R}}_1{\mathrm{R}}_2 \\ =9^2-\left(4\times 18\right) \\ =81-72 \\ =9 \\ {\mathrm{R}}_1-{\mathrm{R}}_2=3......\left(3\right) \\ \mathrm{Add}\left(1\right)\mathrm{and}\left(3\right): \\ 2{\mathrm{R}}_1=12 \\ {\mathbf{R}}_{\mathbf{1}}\mathbf{=}\mathbf{6}\mathbf{}\mathbf{\Omega } \\ \mathrm{Hence}, \\ {\mathrm{R}}_2=9-{\mathrm{R}}_1 \\ =9-6 \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{3}\mathbf{}\mathbf{\Omega } \end{gathered}$$