Question

If $n$ cells each of emf $Î\mu$ and internal resistance $r$ are connected in parallel, then the total emf and internal resistances will be

• A. $Î\mu$, $\frac{r}{n}$
• B. $Î\mu$, $nr$
• C. $nÎ\mu$, $\frac{r}{n}$
• D. $nÎ\mu$, $nr$

Answer 1

Answer: (A)

In the parallel combination,
$\frac{{Î\mu }_{eq}}{r_{eq}}=\frac{{Î\mu }_1}{r_1}+\frac{{Î\mu }_2}{2}+....+\frac{{Î\mu }_n}{r_n}$
$\frac{1}{r_{eq}}=\frac{1}{r_1}+\frac{1}{r_2}+....+\frac{1}{r_n}$
$(âˆ\mu {Î\mu }_1={Î\mu }_2={Î\mu }_3=.....={Î\mu }_n=Î\mu$ and $r_1=r_2=r_3=....r_n=r)$
$∴\frac{{Î\mu }_{eq}}{r_{eq}}=\frac{Î\mu }{r}+\frac{Î\mu }{r}+....+\frac{Î\mu }{r}=n\frac{Î\mu }{r}…\left(i\right)$
$\frac{1}{r_{eq}}=\frac{1}{r}+\frac{1}{r}+....+\frac{1}{r}=\frac{n}{r}$
$r_{eq}=r/n…\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$,
${Î\mu }_{eq}=n\frac{Î\mu }{r}×r_{eq}$
$=n×\frac{Î\mu }{r}×\frac{r}{n}=Î\mu$