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-

 

 

1. Series Combination
2. Parallel Combination
3. 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- the positive terminal of all cells are connected to one common point and all their negative terminals are connected to another common point.

 

Expression For Equivalent EMF-

 

Consider two cells having emfs E₁ and E₂ and internal resistances r₁ and r₂ respectively are connected in parallel combination across an external resistance R as shown-

 

 

Using Kirchoff’s Voltage Law in the loop ABCDEFGA, we have-

 

-E₁ + I₁r₁ + IR = 0

I₁r₁ = E₁ – IR

I₁ = (E₁ – IR) / r₁       ………..(1)

 

Using Kirchoff’s Voltage Law in the loop AHIDEFGA, we have-

 

-E₂ + I₂r₂ + IR = 0

I₂r₂ = E₂ – IR

I₂ = (E₂ – IR) / r₂       ………..(2)

 

Also Read- How to Apply Kirchhoff’s Laws?

 

Adding Equations-01 & 02, we get-

 

(Equation-03)

 

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-

 

Note-01:

 

The equivalent emf of a parallel combination of cells is given by the formula-

 

 

Note-02:

 

In parallel combination of cells, the reciprocal of equivalent internal resistance is equal to the sum of the reciprocals of their individual internal resistances.

 

 

Note-03:

 

The above expression for calculation of equivalent emf is valid only when all the cells assist each other.

If one cell of emf E₂ (say) is turned around, then-

 

 

Note-04:

 

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

 

Next Article-

Joule’s Law of Heating

 

Get more notes & other study material of the Chapter Current Electricity.