Physics - Current Electricity Question with Solution | TestHub

When the cells are connected in series $i_s=\frac{2ϵ}{2r+R}=\frac{2ϵ}{2r+2}$

When they are connected in parallel, the emf is ${ϵ}_p=\frac{\frac{ϵ}{r}+\frac{ϵ}{r}}{\frac{1}{r}+\frac{1}{r}}=ϵ$ and the effective internal resistance will be $r_p=\frac{r\times r}{r+r}=\frac{r}{2}$. Therefore, the current will be,

$i_p=\frac{ϵ}{R+\frac{r}{2}}=\frac{ϵ}{2+\frac{r}{2}}=\frac{2ϵ}{4+r}$

Since, $$\begin{gathered} i_s=i_p \\ \Rightarrow \frac{2ϵ}{2r+2}=\frac{2ϵ}{4+r}\Rightarrow r=2\Omega \end{gathered}$$