Consider two cells of emf ε₁ and ε₂ with internal resistances r₁ and r₂, respectively. The two cells are connected in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is equivalent to a single cell with emf given by:

Concept:

Emf: 

• ​Electromotive force is defined as the electric potential produced by either an electrochemical cell or by changing the magnetic field.
• The unit for electromotive force is Volt.

​Cell:

• ​A cell is a device that develops electric energy by converting chemical energy. 
• The function of a cell in a circuit is that the cell provides electrical energy to the circuit which produces a current in it.​

Cells in parallel combination:

• ​Parallel combination circuits have multiple paths between the terminals.
• In a parallel combination of cells, all the positive terminals of the cells are connected together and the negative terminals of the cells are connected together.

• The equivalent resistance, \(r_{eq}=\frac{r_1r_2}{r_1+r_2}\)   
• The equivalent emf, \(ϵ_{eq}=r_{eq}(\frac{ϵ_1}{r_1}+\frac{ϵ_2}{r_2})\) 

​Calculation:

Consider two cells of emf ε1 and ε2 with internal resistances r1 and r2, respectively. The two cells are connected in parallel by connecting their positive terminals together and connecting their negative terminals together.

The equivalent emf of this combination is calculated as, \(ϵ_{eq}=r_{eq}(\frac{ϵ_1}{r_1}+\frac{ϵ_2}{r_2})\) . . . . . . . . .(1)

The equivalent resistance, \(r_{eq}=\frac{r_1r_2}{r_1+r_2}\)

From equation (1), ϵ_eq = (ε1 r2 + ε2 r1) / (r1 + r2​)

Additional Information Cells in series combination: 

• The cells are said to be connected in series if the positive terminal of the first cell is connected to the negative terminal of the second cell and the negative terminal of the second cell is connected to the positive terminal of the third cell.
• The same current flows through each cell.​

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• The equivalent resistance, r = r1 + r2 +r3 + r4
• The equivalent emf, ϵ = ϵ1 + ϵ2 + ϵ3 + ϵ4