Question

In the circuit shown in figure $E,F,G,H$ are cells of emf $2,1,3$ and $1V$ respectively, and their internal resistances are $2,1,3$ and $1\Omega$ respectively.
Calculate
(a) the potential difference between $B$ and $D$ and
(b) the potential difference across the terminals of each cells $G$ and $H$.

Answer 1

Applying Kirchhoff s second law in loop BADB
$2-2i_1-i_1-1-2(i_1-i_2)=0$ .....(i)
Similarly applying Kirchhoff s second law in loop BDCB
$2(i_1-i_2)+3-3i_2-i_2-1=0$ .....(ii)
Solving Eqs. (i) and (ii), we get
$i_1=\frac{5}{13},i_2=\frac{6}{13}$ and $i_1-i_2=-\frac{1}{13}$
(a) Potential difference between B and D.
$V_B+2(i_1-i_2)=V_D$
$\therefore V_B-V_D=-2(i_1-i_2)=\frac{2}{13}V$
(b) $V_G=E_G-i_2{r}_G=3-\frac{6}{13}\times 3=\frac{21}{13}V$
$V_H=E_H-i_2{r}_H=1+\frac{6}{13}\times 1=\frac{19}{13}V$