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```Effective Grouping of Cells

The flow of current through a medium depends to a large extent on the effective grouping of cells. We first discuss some of the terms associated with this

Internal Resistance: As the name suggests, the resistance which is present in the interior of the circuit is called the internal resistance. It may also be defined as the resistance within the battery or any other voltage source which leads to a fall in the source of voltage whenever the current flows.

External Resistance: Quite opposite to internal resistance is the concept of external resistance. The resistance which is not present internally, like not present in the battery is termed as external resistance.

Now we consider the type of grouping necessary for the current to be maximum:

For effective grouping, the current should be maximum. This implies that the value (mR + nr) should be minimum.

Now, mR + nr =

The second term is non-zero, the term in the parenthesis

(√mR - √nr)2 = 0.

Hence,  mR = nr

So  R = n / m r

Illustration:

There are 27 cells with an internal resistance 0.4 W and an external resistance 1.2 W. What is the most effective way of grouping them?

Solution:

Let there be n cells in series having m parallel branches

mn = 27                                    …… (1)

mR = nr                                    …… (2)

1.2 m = n (0.4)

3m = n                                  …… (3)

From equation (1) and (3), we get m = 3 and n = 9

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