Combination of Cells
Before you go through this article, make sure that you have gone through the previous article on Series Combination of Cells.
We have learnt
 A single cell provides a feeble current.
 In order to get a higher current in the circuit, we use a combination of cells.
 A combination of cells is called a battery.
Cells may be combined together in the following ways
 Series Combination
 Parallel Combination
 Mixed Combination
In this article, we will learn about parallel combination of cells.
Parallel Combination of Cells
The cells are said to be connected in parallel combination when

Expression For Equivalent EMF
Consider two cells having emfs E_{1} and E_{2} and internal resistances r_{1} and r_{2} respectively are connected in parallel combination across an external resistance R as shown
Using Kirchoff’s Voltage Law in the loop ABCDEFGA, we have
E_{1} + I_{1}r_{1} + IR = 0
I_{1}r_{1} = E_{1} – IR
I_{1} = (E_{1} – IR) / r_{1} ………..(1)
Using Kirchoff’s Voltage Law in the loop AHIDEFGA, we have
E_{2} + I_{2}r_{2} + IR = 0
I_{2}r_{2} = E_{2} – IR
I_{2} = (E_{2} – IR) / r_{2} ………..(2)
Also Read How to Apply Kirchhoff’s Laws?
Adding Equations01 & 02, we get
(Equation03)
Now, we wish to replace the above parallel combination of cells with a single equivalent cell of emf E_{eq} and internal resistance r_{eq}.
An equivalent cell is one which supplies the same current to the external resistor as supplied by the individual cells together. 
Replacing the above parallel combination of cells with an equivalent cell, we have
Using Kirchoff’s Voltage Law in the above circuit, we have
E_{eq} + Ir_{eq} + IR = 0
I(r_{eq} + R) = E_{eq}
I = E_{eq} / (r_{eq} + R) ………..(4)
On comparing equations (3) and (4), we get
This is the required expression for equivalent emf & internal resistance of a parallel combination of two cells.
The formula can be extended for n cells in the same way.
Important Notes
Note01:
The equivalent emf of a parallel combination of cells is given by the formula
Note02:
In parallel combination of cells, the reciprocal of equivalent internal resistance is equal to the sum of the reciprocals of their individual internal resistances.
Note03:
The above expression for calculation of equivalent emf is valid only when all the cells assist each other.
If one cell of emf E_{2} (say) is turned around, then
Note04:
If n identical cells each of emf E and internal resistance r are combined in parallel combination, then
Test Your Concepts
Quiz on Parallel Combination of Cells
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