Question

Two cells of emf $4V$ and $2V$ and internal resistance $2\Omega$ and $1\Omega$ respectively are connected in parallel so as to send the current in the same direction through an external resistance of $10\Omega$. Find the potential difference across $10\Omega$ resistor.

Answer 1

Equivalent internal resistance of parallel connection $r_{eq}=\frac{r_1{r}_2}{r_1+r_2}$

$\therefore$ $r_{eq}=\frac{1\times 2}{1+2}=\frac{2}{3}\Omega$

Equivalent emf of cells in parallel connection $E_{eq}=[\frac{E_1}{r_1}+\frac{E_2}{r_2}]r_{eq}$

$\therefore$ $E_{eq}=[\frac{2}{1}+\frac{4}{2}]\times \frac{2}{3}=\frac{8}{3}$ V

Potential difference across $10\Omega$ resistor, $E=\frac{R}{R+r_{eq}}{E}_{eq}$

$\therefore$ $E=\frac{10}{10+\frac{2}{3}}\times \frac{8}{3}=2.5$V