Question

In the circuit shown, the potential difference between $A$ and $B$ is :

• A. $1\text{V}$
• B. $2\text{V}$
• C. $3\text{V}$
• D. $6\text{V}$

Answer 1

The correct option is B $2\text{V}$

Given, $E_1=1V,E_2=2V,E_3=3V,r_1=1\Omega ,r_2=1\Omega \text{and}{r}_3=1\Omega$

As no current is flowing across points A and D, and, B and C, we can write, $V_{AD}=V_{BC}$

$\Rightarrow V_{AB}=V_{CD}=E_{eq}=\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2}+\frac{E_3}{r_3}}{\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}}$

$=\frac{\frac{1}{1}+\frac{2}{1}+\frac{3}{1}}{\frac{1}{1}+\frac{1}{1}+\frac{1}{1}}$

$=\frac{6}{3}=2\text{V}$

Hence, $\left(B\right)$ is the correct answer.