A battery of 24 cells,each of emf 1.5, V and | vedclass

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Question

(A) Let $m$ be the number of rows connected in parallel and $n$ be the number of cells in each row. The total number of cells is $N = n 	imes m = 24$

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$2$ rows of $12$ cells connected in parallel

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(A) Let $m$ be the number of rows connected in parallel and $n$ be the number of cells in each row. The total number of cells is $N = n 	imes m = 24$.The condition for maximum current through an external resistance $R$ is that the total internal resistance of the battery must be equal to the external resistance:$R = \frac{nr}{m}$Given $R = 12\, \Omega$,$r = 2\, \Omega$,and $N = 24$:$12 = \frac{n 	imes 2}{m} \Rightarrow 6m = n$Substitute $n = 6m$ into the total cell equation $n 	imes m = 24$:$(6m) 	imes m = 24$$6m^2 = 24$$m^2 = 4 \Rightarrow m = 2$Now,find $n$:$n = 6 	imes 2 = 12$Thus,there are $2$ rows,each containing $12$ cells connected in series,and these rows are connected in parallel.

$A$ battery of $24$ cells,each of emf $1.5\, V$ and internal resistance $2\, \Omega$,is to be connected to send the maximum current through a $12\, \Omega$ resistor. The correct arrangement of cells will be:

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