Series Combination of Cells | Formula

Combination of Cells-

 

• 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 as a battery.

 

Cells may be connected in the following styles-

 

 

1. Series Combination
2. Parallel Combination
3. Mixed Combination

 

In this article, we will discuss about series combination of cells.

 

Series Combination of Cells-

 

The cells are said to be connected in series combination when the negative terminal of the first cell is connected to the positive terminal of the second cell and so on.

 

Consider two cells of emf E₁ and E₂ and internal resistance r₁ and r₂ respectively are connected across an external resistance R as shown-

 

 

Using Kirchoff’s Voltage Law in the above circuit, we have-

 

-E₁ + Ir₁ – E₂ + Ir₂ + IR = 0

I(r₁ + r₂ + R) = E₁ + E₂

I = (E₁ + E₂) / (r₁ + r₂ + R)         ………..(1)

 

Now, consider the above series combination of cells is replaced by a single cell of emf E_eq and internal resistance r_eq, then equivalent circuit is-

 

 

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)         ………..(2)

 

On comparing equations (1) and (2), we get-

 

 

The same result can be extended for n cells.

 

Characteristics of Series Combination of Cells-

 

Point-01:

 

The equivalent emf of a series combination of cells is equal to the sum of their individual emfs.

 

 

Point-02:

 

The equivalent internal resistance of a series combination of cells is equal to the sum of their individual internal resistances.

 

 

Point-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-

 

 

Point-04:

 

If n identical cells each of emf E and internal resistance r are connected in series combination, then-

 

 

Point-05:

 

If n identical cells each of emf E and internal resistance r are connected in series combination and polarity of m cells is reversed, then-

 

 

However, the equivalent internal resistance still remains the same i.e. nr.

 

Read the next article on-

Parallel Combination of Cells

 

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