Two cells, having the same e.m.f. are connected in series through… - Vidyadip

MCQ

Two cells, having the same $e.m.f.$ are connected in series through an external resistance $R.$ Cells have internal resistances $r_1$ and $r_2\,\, (r_1 > r_2)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of $R$ is

A
$\sqrt {{r_1}{r_2}} $
B
$\;{r_1} + {r_2}$
✓
$\;{r_1} - {r_2}$
D
$\frac{{\;{r_1} + {r_2}}}{2}$

✓

Answer

Correct option: C.

$\;{r_1} - {r_2}$

c
(b) Let the voltage across any one cell is $V$, then

$V = E - ir = E - {r_1}\,\left( {\frac{{2E}}{{{r_1} + {r_2} + R}}} \right)$

But $V = 0$

$==>$ $E - \frac{{2E{r_1}}}{{{r_1} + {r_2} + R}} = 0$

$==>$ ${r_1} + {r_2} + R = 2{r_1}$

$==>$ $R = {r_1} - {r_2}$

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