Q. To get a maximum current through a resistance of $2.5\Omega,\ $one can use $m$ rows of cells each row having $n$ cells. The internal resistance of each cell is 0.5$\Omega$. What are the values of $m$ and $n$ if the total number of cells are 20?
A) $m = 2,\ n = 10$
B) $m = 4,\ n = 5$
C) $m = 5,\ n = 4$
D) $n = 2,\ m = 10$
Explanation
(a) $m\ n = 20$ …(i)
For maximum current $R = \frac{n\ r}{m}$
or $2.5 = n \times 0.5/m\ or\ n = 5m$
From Eq.(i), $m \times 5m = 20\ or\ m^{2} = 4$
or $m = 2.\ $Therefore, $n = 5 \times 2 = 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.