Question

$n$ identical cells, each of emf $\text{E}$ and internal resistance $r$, are joined in series to form a closed circuit. One of the cells is joined with reversed polarity. The potential difference across each cell, except the cell with the reversed polarity, is $\frac{2(\rho -1)\text{E}}{n}$. The value of $\rho$ is(integer only)

Answer 1

$E_{\text{eq}}=(n-1)\text{E}-\text{E}=(n-2)\text{E}$

$r_{\text{eq}}=nr$

$\therefore i=\frac{E_{\text{eq}}}{r_{\text{eq}}}=\frac{(n-2)\text{E}}{nr}$

For each cell,


$\Delta V=E-ir$

$\Rightarrow \Delta V=E-\frac{(n-2)\text{E}}{n}$

$\Rightarrow \Delta V=\frac{2\text{E}}{n}$

Given, $\Delta V=\frac{2(\rho -1)\text{E}}{n}$

$\therefore \rho =2$