Question

In the circuit shown in figure cells of emf $2,1,3$ and $1V$ respectively having resistances $2\Omega ,1\Omega ,3\Omega$ and $1\Omega$ are their internal resistances respectively. The potential difference between D and B (in volts)

• A. $\frac{5}{13}$
• B. $\frac{2}{13}$
• C. $\frac{10}{13}$
• D. $\frac{7}{13}$

Answer 1

The correct option is C $\frac{10}{13}$

Let the current in BAD part is $i$, the current in DB is $i_1$ and the current in DCB is $i_2$.

Apply Kirchhoff’s law at point D, we get

$i=i_1+i_2$ (1)

Apply Kirchhoff’s second law to mesh ABDA, we get

$2i+i+2i_1=2-1$

$3i+2i_1=1$

$3\left(i_1+i_2\right)+2i_1=1$

$3i_2+5i_1=1$ (2)

Apply Kirchhoff’s second law to mesh DCBD, we get

$3i_2+i_2-2i_1=-3+1$

$4i_2-2i_1=-2$ (3)

By solving the equations (2) and (3), we get

$i_1=\frac{5}{13}$

$i_2=\frac{-4}{13}$

The potential difference between D and B is given as,

$V_{DB}=2\times \frac{5}{13}$

$V_{DB}=\frac{10}{13}V$