Question

Find the potential difference (in V) between the points $A$ and $B$ in the circuit shown in the figure.

Answer 1

We assign node $N_3$ as $0V$ and $N_1,N_2$ as $x,y$ volt, respectively. Conservation of charge in isolated system 1.

$5(y-0)+10(y-20)+10\left[\right(y+20)-20]+5\left[\right(y+20)-(-10\left)\right]=0$or $30y=50$ or $y=\frac{3}{5}V$

Conservation of charge in isolated system 2

$5\left[\right(x+20)-0]+10\left[\right(x+20)-10]+5[x-10]+10[x-(-10\left)\right]=0$

or $30x=-250$ or $x=\frac{-25}{3}V$

Thus

$V_A-V_B=\frac{5}{3}-\left(\frac{-25}{3}\right)=10V$