Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance 1.5 Ω. Find the value of internal resistance of each cell.

Question

Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance 1.5 Ω. Find the value of internal resistance of each cell. (A) 1 Ω (B) 0.5 Ω (C) zero (D) 1.5 Ω

Tardigrade Admin · Accepted Answer

Let n cells be in series and m in parallel, then (n E/R+n r)=(E/R+(r)m) ⇒ n[R+(r/m)]=R+ n r ⇒ n R m +n r=R m+ m n r ⇒ 6+2 r=3+4 r ⇒ 2 r=3 ⇒ R=1.5 Ω

Q. Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance $1.5 Ω$ . Find the value of internal resistance of each cell.

$1 Ω$

$0.5 Ω$

zero

$1.5 Ω$

Let $n$ cells be in series and $m$ in parallel, then
$\frac{n E}{R + n r} = \frac{E}{R + \frac{r}{m}}$
$\Rightarrow n [R + \frac{r}{m}] = R + n r$
$\Rightarrow n R m + n r = R m + mn r$
$\Rightarrow 6 + 2 r = 3 + 4 r$
$\Rightarrow 2 r = 3 \Rightarrow R = 1.5 Ω$

Q. Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance 1.5Ω. Find the value of internal resistance of each cell.

1Ω

0.5Ω