# For the circuit shown, with $R_{1}=1.0\; \Omega,$ $R_{2}=2.0\; \Omega,$ $E_{1}=2\; V$ and $E_{2}=E_{3}=4\; V,$ the potential difference between the points 'a' and 'b' is approximately(in V) :Option 1)$2.7$Option 2)$3.7$Option 3)$3.3$  Option 4)$2.3$

S solutionqc

$R_{1}=1\: \Omega , E_{1}=2\; v$

$E_{2}=4\; v, E_{3}=4\; v, R_{2}=2\; \Omega$

For parallal combination of cells

$\varepsilon _{a}=\frac{\frac{\varepsilon _{1}}{r_{1}}+\frac{\varepsilon _{2}}{r_{2}}+\frac{\varepsilon _{3}}{r_{3}}....}{\frac{1}{r_{1}}+\frac{1}{r_{2}}+\frac{1}{r_{3}}.....}=\frac{\frac{2}{2}+\frac{4}{2}+\frac{4}{2}}{\frac{1}{2}+\frac{1}{2}+\frac{1}{2}}$

$\varepsilon _{a}=\frac{10}{3}=3.3\; V$

Option 1)

$2.7$

Option 2)

$3.7$

Option 3)

$3.3$

Option 4)

$2.3$

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