Question

In the network shown the potential difference between A and B is:

$(R=r_1=r_2=r_3=1\Omega ,E_1=3V,E_2=2V,E_3=1V)$

• A. 1 V
• B. 2 V
• C. 3 V
• D. 4 V

Answer 1

The correct option is B 2 V

There is no current flows through the resistor $R$.

So, the potential difference across $AB$ is $V=\frac{\frac{E_1}{r_1}+\frac{E_2}{r_2}+\frac{E_3}{r_3}}{\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}}$

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