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:

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=(r/n)  (C)  R=n2r  (D)  R=r

Tardigrade Admin · Accepted Answer

Current when cells are connected in series is=(n E/n r+R) in parallel ip=(n E/r+n R) According to question is=ip (n E/n r+R) =(n E/r+n R) r+n R =n r+R (n-1) R =r(n-1) ⇒ R =r

Q. $n$ 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:

$R = n r$

$R = \frac{r}{n}$

$R = n^{2} r$

$R = r$

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 $i_{s} = i_{p}$
$\frac{n E}{n r + R} = \frac{n E}{r + n R}$
$r + n R = n r + R$
$(n - 1) R = r (n - 1)$
$\Rightarrow R = r$

Q. 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:

R=nr

R=nr​

R=n2r

R=r