Question

The circuit given below consists of cells with their internal resistance,

$\left(i\right)$ The equivalent emf between the terminals $A$ and $B$ is

• A. $\frac{24}{13}\text{V}$
• B. $\frac{37}{13}\text{V}$
• C. $\frac{36}{13}\text{V}$
• D. $\frac{49}{13}\text{V}$

Answer 1

The correct option is D $\frac{49}{13}\text{V}$

The effective emf between $C$ and $B$
$E_{CB}=\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2}+\frac{E_3}{r_3}}{(\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3})}=\frac{\frac{2}{2}+\frac{3}{3}+\frac{4}{4}}{(\frac{1}{2}+\frac{1}{3}+\frac{1}{4})}=\frac{36}{13}$
The effective emf between $A$ and $B$ is
$\therefore E_{AB}=E_{AC}+E_{CB}$
$E_{AB}=1+\frac{36}{13}$
$E_{AB}=\frac{49}{13}\text{V}$