Question

$100$ cells, each of e.m.f. $5V$ and internal resistance $1\Omega$, are to be arranged so as to produce maximum current in a $25\Omega$ resistance. Each row is to contain equal number of cells. The number of rows should be ______.

Answer 1

For maximum current, the external resistance must be equal to the total internal resistance.

$⟹\frac{nr}{m}=R$, where, {$R:$External resistance, $n:$no of cells in each row, $m:$no of rows, $r:$internal resistance of one cell.}

$⟹\frac{n}{m}\left(1\right)=2$

$⟹\frac{n}{m}=25\to \left(1\right)$

Now at $Q$, there are totl $100$ bulbs and each row must contain equal no of bulbs.

$⟹n\times m=100\to \left(2\right)$

Using eq.$\left(1\right)$ and $\left(2\right),n=30,m=2$

No o rows $m=2$