Question

To get maximum current through a resistance of 2.5Ω, one can use ‘m′ rows of cells, each containing ‘n′ cells connected in series. The internal resistance of each cell is 0.5Ω. What are the values of n and m if the total numbers of cells are 45?

Answer 1

mn = 45
for maximum current R = nr/m
=>2.5=(0.5)n/m
=>5m=n
=>5m=45/m
=>m^2=9
=>m=3
then n=15
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Answer 2

To get maximum current through a resistance of 2.5Ω, one can use ‘m′ rows of cells, each containing ‘n′ cells connected in series. The internal resistance of each cell is 0.5Ω.The values n will be 15 and m will be 3.

• This question is based on the maximum power theorem and combinations of non-ideal cells.
• According to maximum power theorem, to get maximum current, net resistance must be equal to given resistance i.e, 2.5 ohms.

      Therefore,              $\frac{n*0.5}{m}$

                        and  n*m = 45

                      gives us, n=15  and m=3