Consider N=n_(1)n_(2)indentical cells, each of emf(epsilon) and internal resistance r. Suppose n_(1) cells are joined in series to forn a line and n_(2) such are connected in parallel. The combination drives a current in an external resistance R.(a) find the current in the external resistance, (b) Assuming that n_(1)and n_(2) can be continuously varied, find the relation between n_(1) ,n_(2) R and r for which the current in R in maximum.

Consider N=n_(1)n_(2)indentical cells, each of emf(epsilon) and intern

1.	Consider N=n_(1)n_(2)indentical cells, each of emf(epsilon) and internal resistance r. Suppose n_(1) cells are joined in series to forn a line and n_(2) such are connected in parallel. The combination drives a current in an external resistance R.(a) find the current in the external resistance, (b) Assuming that n_(1)and n_(2) can be continuously varied, find the relation between n_(1) ,n_(2) R and r for which the current in R in maximum.
Answer» Solution : Total e.m.f. = ` n_1` EIN one row Total e.m.f. in all rows = `n_1 E` Total RESISTANCE in one row = `n_1`r/`n_2` Net resistance = `R+ (n_1)r/(n_2)` ` So, Current = R + ((n_1)r/n_2)` ` (b) L = ((n_1)(n_2)E/ n_2 R + n_2 r)` For, L = MAX ` (n_1)r + (n_2)R = minimum ` ` rArr ((sqrt (n_1)r)- (sqrt(n_2)R))^2 + 2((sqrt(n_1)R(n_2)R)) = min. ` It is minimum when, ` (sqrt(n_1)r) = (sqrt(n_2)R) ` ` n_1r = n_2R` L is maximumwhen, ` n_1r = n_2R` .

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