Q. A battery of 24 cells, each of emf $1.5\ V$ and 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
Explanation
(a) Suppose $m$ rows are connected in parallel and each row contains $n$ identical cells (each cell having $E = 15\ V$ and $r = 2\Omega$)
For maximum current in the external resistance $R,$ the necessary condition 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 equations (i) and (ii) $n = 12$ and $m = 2\ i.e.$ 2 rows of 12 cells are connected in parallel
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.