Two batteries \(E_1\) (emf 6 V, internal resistance : \(0.5\Omega\)) and \(E_2\) (emf : 12 V, internal resistance : \(1.0\Omega\)) are connected in parallel by connecting their positive terminals to point A and negative terminals to point B. A third battery \(E_3\) (emf : 6 V, internal resistance :\((\frac{2}{3})\Omega\)) is connected in series with this combination by connecting its positive terminal to B.
Select one correct option: