Question

In the circuit shown in figure, cells of emf 2,1,3 and $1\text{V}$, respectively and resistances $2\Omega ,1\Omega ,3\Omega$ and $1\Omega$ are their internal resistances respectively. The potential difference between $D$ and $B$ is given as $\frac{n}{13}$ volts. Find $n$.

Answer 1

by KCL
$\frac{x-2}{3}+\frac{x-3}{2}+\frac{x-1}{4}=0$
$4x-8+6x-18+3x-3=0$
$13x=29$
$x=\frac{29}{13};V_{BD}=\frac{10}{13}\text{V}$