Question

The circuit given below consists of cells with their internal resistance

$\left(iii\right)$ If the polarity of cell of $4\text{V}$ is reversed, the equivalent emf between the terminals $A$ and $B$ is

• A. $\frac{1}{13}\text{V}$
• B. $\frac{37}{13}\text{V}$
• C. $\frac{25}{13}\text{V}$
• D. $\frac{12}{13}\text{V}$

Answer 1

The correct option is C $\frac{25}{13}\text{V}$

If the polarity of cell $4\text{V}$ is reversed
$E_{AB}=E_{AC}+E_{AB}=1+\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2}-\frac{E_3}{r_3}}{(\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3})}$
$E_{AB}=1+\frac{\frac{2}{2}+\frac{3}{3}-\frac{4}{4}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}=1+\frac{1}{\left(\frac{13}{12}\right)}$
$E_{AB}=\frac{25}{13}\text{V}$