Question

$n$ cells each of emf $\varepsilon$ and internal resistance $r$ send the same current through an external resistance $R$ whether the cells are connected in series or in parallel. Then

• A. R=nr
• B. R=r
• C. r=nR
• D. $R=\sqrt{n} r$

Answer 1

Answer: (B)

Cells in series,
Current through the external resistance,
$I=\frac{n \varepsilon}{R+n r}$
Cells in parallel, $I=\frac{\varepsilon}{R+\frac{r}{n}}=\frac{n \varepsilon}{n R+ r}$
According to problem, $\frac{n \varepsilon}{R+n r}=\frac{n \varepsilon}{n R+ r}$
or, $R+n r=n R +r \Rightarrow R(1-n)=r(1-n)$
$\Rightarrow R=r$