324 identical galvanic cells, each of internal resistance 9 ohm are arranged as several in series, groups of cell connected in parallel The arrangement has been laid out so that power output in an externally connected resistance of value 4 ohm is maximum. If n cells are connected in every series group that form parallel combination, then find value of n.

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Question :

324 identical galvanic cells, each of internal resistance 9 ohm are arranged as several in series, groups of cell connected in parallel The arrangement has been laid out so that power output in an externally connected resistance of value 4 ohm is maximum. If n cells are connected in every series group that form parallel combination, then find value of n.

Answer :

It is asked in question to find value of n such that power transfer to externally connected resistance of value 4 ohm is maximum. 
According to maximum power transfer theorem, power transfer to external resistance (4 ohm) will be maximum when value of resistance of combination of 324 cells is equal to 4 ohm 
i.e. Source resistance = load resistance

In above image n= Number of resistances in series
m=Number of resistance groups in parallel
Now, n cells are connected to each series group. So resistance of one series group is nR. 
There are m parallel groups. So total resistance = nR/m. 
Now for maximum power transfer nR/m = 4
And finally n=12.

So 12 resistances should be connected in each series group.
Answer : n=12

If you have any queries regarding above solution then please comment below. Thank you! 

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