Question

$n$ cells each of emf $\epsilon$ 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,
$I=\frac{n\epsilon }{R+nr}$
Cells in parallel, $I=\frac{\epsilon }{R+\frac{r}{n}}=\frac{n\epsilon }{nR+r}$
According to problem, $\frac{n\epsilon }{R+nr}=\frac{n\epsilon }{nR+r}$
or, $R+nr=nR+r\Rightarrow R(1-n)=r(1-n)$
$\Rightarrow R=r$