Two batteries of emf E₁ and E₂ (E₂ > E₁) and internal resistances r₁ and r₂, respectively are connected in parallel as shown in the figure. Which of the following options is correct ?

The equivalent internal resistance of two cells between A and B, ${\mathrm{R}}_{\mathrm{eq}}=\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{{\mathrm{r}}_1+{\mathrm{r}}_2}$ (Parallel combination case of resistances)

If E is the equivalent emf of the two cells in parallel between A and B, then

$\frac{{\mathrm{E}}_{\text{eq }}}{{\mathrm{R}}_{{\mathrm{v}}_0}}=\frac{{\mathrm{E}}_1}{{\mathrm{r}}_1}+\frac{{\mathrm{E}}_2}{{\mathrm{r}}_2}=\frac{{\mathrm{E}}_1{\mathrm{r}}_2+{\mathrm{E}}_2{\mathrm{r}}_1}{{\mathrm{r}}_1{\mathrm{r}}_2}$

$\therefore {\mathrm{E}}_{\mathrm{eq}}=\left(\frac{{\mathrm{E}}_1{\mathrm{r}}_2+{\mathrm{E}}_2{\mathrm{r}}_1}{{\mathrm{r}}_1{\mathrm{r}}_2}\right){\mathrm{R}}_{\mathrm{eq}}=\frac{{\mathrm{E}}_1{\mathrm{r}}_2+{\mathrm{E}}_2{\mathrm{r}}_1}{\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)}$

$\text{ As, }{\mathrm{E}}_2>{\mathrm{E}}_1\Rightarrow {\mathrm{E}}_1<\mathrm{E}<{\mathrm{E}}_2{\text{ [For all values of r}}_{\text{1}}{\text{ and r}}_{\text{2}}\text{]}$