Question

What is the potential difference between points B and D in the given circuit.

• A. 1/13 A
• B. 1/14 A
• C. 1/15 A
• D. None of the above

Answer 1

The correct option is A

1/13 A

We can treat the resistors on the arms with the cells as internal resistances and apply cell combination formula and simplify.
On branch DAB, we have,
$E=E_1+E_2=2+(-1)=1V.R=R_1+R_2=1+2=3\Omega$.
We can apply the same idea to the next branch and arrive at the following simplified circuit:


Now we see that these two cells with internal resistances are in parallel. We can quickly solve these too.
$E=\frac{E_1{r}_2+E_2{r}_1}{r_1+r_2}E=\frac{(-4+6)}{7}E=\frac{2}{7V}r=\frac{12}{7}\Omega$
Thus we have reduced it to

Now we can easily solve the current through 2 $\Omega$ to be $\frac{2}{26}A$
or
i=$\frac{1}{13}A$