Question

Two cell of emf $6V$ and $4V$ having internal resistance $3\Omega$ and $2\Omega$ respectively are connected in parallel so all to send a current through extend resistance of $8\Omega$ in the same direction. Find the current through the cells and the potential difference across $8\Omega$ Resistor.

Answer 1

$\frac{E_{eff}}{r_{eff}}=\frac{E_1}{r_1}+\frac{E_2}{r_2}$

$r_{eff}=\frac{r_1{r}_2}{r_1+r_2}=\frac{\left(3\right)\left(2\right)}{3+2}=6/5\Omega$

$\frac{E_{eff}}{6/5}=\frac{6}{3}+\frac{4}{2}$

$\frac{5}{6}{E}_{eff}=2+2=4$

$E_{eff}=\frac{24}{5}$

$I=\frac{\frac{24}{5}}{\frac{6}{5}+8}$ $=\frac{\frac{24}{5}}{\frac{46}{5}}=\frac{24}{46}$

$I_8=\frac{24}{46}\times 84$

$=\frac{96}{23}V$