Question

Two cells ${\epsilon }_1$ and ${\epsilon }_2$ connected in opposition to each other as shown in figure. The cell ${\epsilon }_1$ is of emf $9V$ and internal resistance $3\Omega$ the cell ${\epsilon }_2$ is of emf $7V$ and internal resistance $7\Omega$. The potential difference between the points A and B is?

• A. $8.4$V
• B. $5.6$V
• C. $7.8$V
• D. $6.6$V

Answer 1

The correct option is A $8.4$V

Given: The emf and internal resistance of the first cell is $9V\&3\Omega$.

The emf and internal resistance of the second cell is $7V\&7\Omega$.

To find: The potential difference between the points A and B.

The current flowing through the combination of the cells is given by:

$I=\frac{\Delta \epsilon }{r_1+r_2}$

Here, $r_1$ and $r_2$ are the internal resistances of the cells.

$I=\frac{9-7}{3+7}$

$\Rightarrow \frac{2}{10}=0.2A$

Now the potential difference between the point A and B will be the potential drop across the second cell.

Potential drop across the second cell is $V_2+(I\times r_2)$

$\Rightarrow 7V+(0.2\times 7)$

$\Rightarrow 8.4V$

Option $A$ is correct.