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(C) The total number of cells is given by $mn = 24$. For maximum current in a mixed grouping of cells,the external resistance $R$ must be equal to the

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$12, 2$

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(C) The total number of cells is given by $mn = 24$. 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 equivalent internal resistance is given by $r_{eq} = \frac{mr}{n}$. Given $R = 3\, \Omega$ and $r = 0.5\, \Omega$,we have $\frac{m(0.5)}{n} = 3$. This simplifies to $0.5m = 3n$,or $m = 6n$. Substituting $m = 6n$ into the equation $mn = 24$: $(6n)n = 24 \Rightarrow 6n^2 = 24 \Rightarrow n^2 = 4 \Rightarrow n = 2$. Now,substituting $n = 2$ into $m = 6n$: $m = 6(2) = 12$. Thus,$m = 12$ and $n = 2$.

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