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(A) For maximum current in a mixed grouping of cells,the external resistance $R$ must be equal to the equivalent internal resistance of the combinatio

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$m= 3, n = 15$

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(A) For maximum current in a mixed grouping of cells,the external resistance $R$ must be equal to the equivalent internal resistance of the combination.The condition for maximum current is $R = \frac{nr}{m}$,which implies $mR = nr$.Given:External resistance $R = 2.5\,\Omega$Internal resistance of each cell $r = 0.5\,\Omega$Total number of cells $N = m 	imes n = 45$.Substituting the values into the condition $mR = nr$:$m 	imes 2.5 = n 	imes 0.5$$5m = n$.Now,substitute $n = 5m$ into the total number of cells equation $mn = 45$:$m(5m) = 45$$5m^2 = 45$$m^2 = 9$$m = 3$.Then,$n = 5 	imes 3 = 15$.Thus,$m = 3$ and $n = 15$.

To get maximum current through a resistance of $2.5\,\Omega$,one can use $m$ rows of cells,each row having $n$ cells. The internal resistance of each cell is $0.5\,\Omega$. What are the values of $n$ and $m$ if the total number of cells is $45$?

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