Question

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

• A. 2 rows of 12 cells connected in parallel
• B. 3 rows of 8 cells connected in parallel
• C. 4 rows of 6 cells connected in parallel
• D. All of these.

Answer 1

The correct option is A 2 rows of 12 cells connected in parallel

Suppose $m$ rows are connected in parallel and each row contain $n$ identical cells (each cell having $E=15Vandr=2\Omega$)For maximum current in the external resistance $R,$ the neccessary is $R=\frac{nr}{m}$$\Rightarrow 12=\frac{n\times 2}{m}\Rightarrow n=6m$ .........(i)

Total cells $=24=n\times m$ .........(ii)

On solving equation (i) and (ii) n$=12$ and $m=2$

i.e. $2$ rows of $12$ cells are connected in parallel.