Question

To get maximum current in a resistance of $3ohms$, one can use $n$ rows of $m$ cells (connected in series) connected in parallel. If the total number of cells is $24$ and the internal resistance of a cell is $0.5ohms$ then

• A. $m=12,n=2$
• B. $m=8,n=3$
• C. $m=2,n=12$
• D. $m=6,n=4$

Answer 1

Answer: (A)

Let, we connect $24$ cells in n rows of m cells, then if $I$ is the current in external circuit then
$I=\frac{mE}{mr/n+R}$ ....(1)
For I to be maximum, $(mr+nR)$ should be minimum.
It is minimum for $R=\frac{mr}{n}$ ....(2)
So maximum current in external circuit is $I=\frac{mE}{2R}$......(3)
here $R=3,r=0.5$ so equation (2) become $\frac{m}{n}=6$
so $n=2,m=12$