Question

To get maximum current in a resistance of 3 ohms, 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 0.5 ohms then

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

Answer 1

The correct option is A $m=12,n=2$

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 $\frac{m}{n}=6$

$\Rightarrow m=12andn=2$