Question

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

• A. 6 V
• B. 1 V
• C. 3 V
• D. 2 V

Answer 1

Answer: (D)

Potential difference across $AB$ will be equal to battery equivalent across $CD$
$V_{AB} =V_{CD} = \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} = 2V $