Two cells of emf 1 V and 2 V and internal resistance \(2 \Omega\) and \(1 \Omega\), respectively, are connected in series with an external resistance of \(6 \Omega\). The total current in the circuit is \(\mathrm{I}_1\). Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is \(I_2\). The value of \(\left(\frac{I_1}{I_2}\right)\) is \(\frac{x}{3}\). The value of \(x\) is _____.

\(\begin{aligned} & \varepsilon_{\mathrm{eq}}=3 \\ & \mathrm{R}_{\mathrm{eq}}=9 \\ & \mathrm{i}_1=\frac{3}{9}=\frac{1}{3}\end{aligned}\)

\(\varepsilon_{\mathrm{eq}}=\frac{\frac{\varepsilon_1}{\mathrm{r}_1}+\frac{\varepsilon_2}{\mathrm{r}_2}}{\frac{1}{\mathrm{r}_1}+\frac{1}{\mathrm{r}_2}}\)
\(\varepsilon_{\mathrm{eq}}=\frac{\frac{1}{2}+\frac{2}{1}}{\frac{1}{2}+\frac{1}{1}}=\frac{5}{3}\)
\(\begin{aligned} & \mathrm{r}_{\text {equ }}=\frac{2 \times 1}{3}+6=\frac{20}{3} \\ & \mathrm{i}_2=\frac{1}{4} \Rightarrow \frac{\mathrm{i}_1}{\mathrm{i}_2}=\frac{4}{3}\end{aligned}\)