12 cells each of emf 1.5 v and internal resistance 0.5 ohm are arranged in m rows each containing n cells. Calculate the value of n and m for which this combination would send maximum current though 1.5 ohm

Dear Student,

Please find below the solution to the asked query:

Given that the circuit is having m rows & n cells for each row. Therefore, the effective emf of each branch is,

εrow=nε=1.5n V

Internal resistance of each branch is,

rrow=nr=0.5 n Ω

Now, m such rows are there. So, the effective emf & Internal Resistance of the whole circuit is,

1req=mnrreq=nrm=0.5×nm Ω&εeqreq=mnεnrεeq=mε×req=m×1.5×0.5nmεeq=0.75n V

Therefore, the current through the resistor R=1.5 Ω is,

I=εeqR+req=0.75n1.5+0.5nm=0.75mn1.5m+0.5n=91.5m+0.5nFor Imax  ddm1.5m+0.5n=0ddm1.5m+0.5×12m=0ddm1.5m2+6m=01.5m2+6-m3mm2=01.5m2+6-3m2=01.5m2=6m=2n=6

Hope this information will clear your doubts about the topic.

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