Question

For the circuit shown, calculate the potential difference between points $B$ and $D$.

Answer 1

According to Kirchhoff's first law the distribution of currents is shown in fig.
Applying Kirchhoff's second law to mesh BADB,
$-2(i-i_1)+2-1-1.(i-i_1)+2i_1=0$
$\Rightarrow 3l-5l1=1$.....(i)Applying Kirchhoff's law to mesh DCBD,
$-3i+3-1-1\times i-2i_1=0$
$\Rightarrow 4i+2i_1=2$
or
$2l+l_1=1$..........(ii)
Multiplying equation (ii) with 5, we get
$10i+5i1=5%%........(iii)
Adding (i) and (iii), we get
$13i=6\Rightarrow i=\frac{6}{13}A$
From (ii), $i=1-2i=1-\frac{12}{13}=\frac{1}{13}A$
Potential difference between Band D is
$V_B-V_D=i_1\times 2=\frac{2}{13}V$