Suppose 3 cells are connected in parallel having emf of ε₁, ε₂, and ε₃ and internal resistance r₁, r₂, and r₃ are connected in parallel as shown in figure

Let V(B) and V(C) are the potentials across B and C terminals. Consider the first cell, the potential difference across its terminals is V(B) – V(C)

V_BC ≡ V(B) – V(C) = ε₁ – Ir₁ (potential difference across cell 1)

V_BC ≡ V(B) – V(C) = ε₂ – Ir₂ (potential difference across cell 2)

V_BC ≡ V(B) – V(C) = ε₃ – Ir₃ (potential difference across cell 3)

From the above figure I₁, I₂, and I₃ are leaving from the positive electrodes of the cells. At the point B I₁, I₂, and I₃ are added together and give the resultant current I

The equivalent combination by a single cell A and D of emf V_AD = ε_eq – Ir_eq ------- (4)

Eq(4) and Eq(3) should be the same

We can rewrite the equation in a simpler way