**Why cell combination needed?**

A cell is an electrical element which produces current and a battery is a set of some cells with series or parallel connection. A cell is an active element.

To increase the rate of current and voltage supply, cells are connected as manner in series or parallel or mix combination. Internal resistance of those cells is important factor while making combination to increase voltage or current.

Suppose we are in a place where electricity supply is not available. In this situation we have to use cells for generating electricity. After using cells for a long time battery voltage goes low so that we cannot play television. In this time if we know the internal resistance of cells and external resistance of the circuit which is television resistance here. Then we can arrange the cells in a combination such we can run the television again and watch TV. Which combination has to create that will depend upon internal resistance of cells and TV resistance.

**Figure:** Practical cell

There are three cells shown in above image in real life.

**Combination of Cell**

There mainly two basic combinations of cells are i) series connection and ii) parallel connection. Another combination can be possible which is called iii) mix combination. It is mix combination of series and parallel connection.

**i) Cells in Series
**

Positive terminal of a cell is connected to another cell negative terminal is called series connection of battery. In this way many cell can be connected in series.

In other words if some cell are connected with one common point is called series connection.

**Figure:** Series combination of cells

**Figure:** Practical cell in series connection

If n number of cell has same electromotive force E, internal resistance r connected in series with a external resistance R as shown in figure. As the cells are connected in series so flow of current of all cell is the same direction.

Total electromotive force of the circuit = E + E + E + …….. + n^{th} = nE

Equivalent internal resistance of the circuit = r + r + r + ……. + n^{th} = nr

Internal resistance of the cells and external resistance R are connected in series so that total resistance of this circuit = nr + R

According to Ohm’s law current flow of the circuit,

Connection of some cell in this way is called battery. Total current I_{S} is series current of battery.

**How series combination is useful?**

- The series combination of cell is useful one for one condition. If R»nr then the series combination is useful. If external resistance of the circuit is more and more greater than the internal series resistance of the cells then series combination of cell will give high current. If R is more greater than nr, avoiding nr we get the equation as below,

That is to say one single cell current increases n times more applying this method.

We will get high current from series combination battery if external resistance is more and more greater than internal resistance of battery. The efficiency of battery increases in this situation and we get high current.

- If internal resistance of battery is more and more greater than external resistance than the efficiency of the battery does not raise. At this time series combination of cell is totally useless.

**ii) Cells in parallel
**

When some cells positive terminal are connected and negative terminal also connected then the combination of the cells is called parallel combination of cell.

In other words if some cells are connected such way that they have two common points positive terminals of those cells shorted and negative terminals also shorted is called parallel combination of cell.

**Figure:** Parallel combination of cells

**Figure:** Parallel connection of cell if the two terminal are shorted with wire

Suppose, n number of cell are connected parallelly with a resistance R.

Electromotive force of each cell = E

Internal resistance of each cell = r

In figure positive terminals are connected in A points and negative terminals are connected in B points. As the cells are connected in parallel their internal resistance also connected in parallel. Equivalent internal resistance of the combination,

This equivalent internal resistance r_{p} is connected in series with external resistance R.

So that total resistance of the circuit = R + r_{p} = R + (r/n)

Total current of the circuit is I_{p} then according to Ohm’s Law,

**How parallel connection useful?**

- Parallel combination of cell is useful only for one condition that is if r » R then we can neglect nR and get,

In this situation efficiency of battery improves. It produces more current than before they are individual cell.

- If R » r that means if external resistance value R is more and more greater than equivalent internal resistance value r
_{p}then this parallel combination is totally useless.

**iii) Mix combination of cell**

If some cell is connected in series in some rows and the total rows are connected in parallel then the combination is called mix combination of cell.

**Figure:** Cells in mix combination

Consider, the combination has m number row, n number cell.

Each cell electromotive force = E

Internal resistance of each cell = r

The combination is connected with a external resistance R.

Total electromotive force of the cells is = E_{m}

Equivalent internal resistance of the cells = r_{m}

Total current of the combination = I_{m}

From Ohm’s Law,

Each row has n number cell so total electromotive force of a row = nE

And all row are connected in parallel so mix combination electromotive force E_{m} = nE.

Again each row cells internal resistance are connected in series and those series connection also connected in parallel and become mix. Series internal resistance r_{s} = nr. Mix combination internal equivalent resistance,

Where, N = m×n = total cell number