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12 cells of each of emf 1.5 V and intern...

12 cells of each of emf 1.5 V and internal resistance `0.5 Omega` are arranged in m rows each containing n cells connected in series. Calculate the values of n and m for which this combination would send maximum current through an external resistance of `1.5 Omega` . What is the value of the maximum current?

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According to the question
`mn = 12 " "……(i)`
Now , current along the external resistance R is maximum with .
`R = (nr)/(m)` (r is the internal resistance )
`rArr " "1.5 = (n xx 0.3)/(m) rArr n = 3 m `
From Eqs. (i) and (ii) , we have
m = 2 , n = 6
Values of maxium current in the circuit.
`I = (nE)/((nr)/(m) + R) = (6 xx 1.5)/(6 xx (0.5)/(2)+1.5) = (6 xx 1.5)/(2(1.5)) = 3A`
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