m' cells each of emf E and internal resistance 'r' are connected in parallel. What is the total emf and internal resistance? Under what conditions is the current drawn from mixed grouping of cells maximum?

Explanation

Cells in parallel :
(1) When 'm' identical cells each of emf `epsilon` and internal resistance I are connected to the external resistor of resistance R as shown in fig., then the cells are connected in parallel.
(2) As the cells are connected in parallel, their equivalent internal resistance `r_(p)` is given by
`(1)/(r_(P)) = (1)/(r ) + (1)/(r )` +........upto m terms `= (m)/(r )`
`:. r_(P) = (r )/(m)`
(3) As R and `r_(P)` are in series so total resistance in the circuit `= R + (r )/(m)`
(4) In parallel combination of identical cells, the effective emf in the circuit is equal to the emf due to a single cell, becasue in this combination, only the size of the electrodes increases but not emf.
(5) Therefore, current in the resistance R is given by `I = (epsilon)/(R + (r )/(m)) = (m epsilon)/(m R + r)`
(6) When the external resistance is negligible is comparison to the internal resitance `(R lt lt r)` the current drawn from mixed grouping of cells a maximum.