Question

$n $ equal cells having e.m.f. $E$ and internal resistance $r$, are connected in circuit of a resistance $R$. Same current flows in circuit either they connected in series or parallel, if:

• A. $ R=nr $
• B. $ R=\frac{r}{n} $
• C. $ R=n^{2}r $
• D. $ R=r $

Answer 1

Answer: (D)

Current when cells are connected in series
$i_{s}=\frac{n E}{n r+R}$
in parallel $i_{p}=\frac{n E}{r+n R}$
According to question $i_{s}=i_{p}$
$\frac{n E}{n r+R} =\frac{n E}{r+n R} $
$r+n R =n r+R $
$(n-1) R =r(n-1) $
$\Rightarrow R =r$