(i) `text(In series)`
In this combination of cells negative end of each cell is connected to the positive end of the next cell.
Let n cells each of internal resistance `r` and emf `E` are connected in series.
So, total emf `= nE ` and total internal resistance `= nr.`
Current taken from the combination
`i = (nE)/(nr +R)`
• If `nr < R,` i.e. total internal resistance of cell is less than the external resistance, then the current taken from the combination is n times the current taken from one cell.
• If `nr > > R.` i.e. total internal resistance of cells is greater than the external resistance. then the current taken from the combination is same as that from one cell. So, there is no benefit, joining the cells of high internal resistance in series order.
(ii) `text(In parallel ) ` In this combination positive terminals of all the cells arc connected to one point and negative terminals to the other point.
• Let `n` cells each of internal resistance rand of emf `E` are connected in parallel. Then. emf of combination `= E` and total internal resistance `= r/n`
Current taken from the combination
`i = (nE)/(r + nR)`
• If `r/n >> R` i.e. total internal resistance of cell is greater than external resistance, then current taken from the combination is n times that from one cell.
• If `r/n >> R` i.e. total internal resistance of cell is less than external resistance, then current taken from the combination is equal to that from one cell. So, there is no benefit of connecting cells of low internal resistance in parallel.
`(iii) text(Mixed grouping)` In this combination, a certain number of cells are connected in various series and all such series are then connected in parallel. Number of cells `= mn`
emf of combination `= nE`
Total internal resistance `= (nr)/m`
Current taken in external resistance,
`i = (mnE)/( nr + mR)`
For maximum current in the circuit mR = nr.
If two cells oppose each other, then current taken from them `I = (E_1 -E_2)/(r_1 +r_2 +R)`
Similarly, if cells support each other, then `I = (E_1 +E_2)/(r_1 +r_2 +R)`
Charging current of a cell is given by
`i = text(emf of charger - emf of cell)/text(total resistance of the circuit)`
In a battery of N cells each of emf E, if n cells arc wrongly connected, then net emf,
`E' =NE - 2nE`
(i) `text(In series)`
In this combination of cells negative end of each cell is connected to the positive end of the next cell.
Let n cells each of internal resistance `r` and emf `E` are connected in series.
So, total emf `= nE ` and total internal resistance `= nr.`
Current taken from the combination
`i = (nE)/(nr +R)`
• If `nr < R,` i.e. total internal resistance of cell is less than the external resistance, then the current taken from the combination is n times the current taken from one cell.
• If `nr > > R.` i.e. total internal resistance of cells is greater than the external resistance. then the current taken from the combination is same as that from one cell. So, there is no benefit, joining the cells of high internal resistance in series order.
(ii) `text(In parallel ) ` In this combination positive terminals of all the cells arc connected to one point and negative terminals to the other point.
• Let `n` cells each of internal resistance rand of emf `E` are connected in parallel. Then. emf of combination `= E` and total internal resistance `= r/n`
Current taken from the combination
`i = (nE)/(r + nR)`
• If `r/n >> R` i.e. total internal resistance of cell is greater than external resistance, then current taken from the combination is n times that from one cell.
• If `r/n >> R` i.e. total internal resistance of cell is less than external resistance, then current taken from the combination is equal to that from one cell. So, there is no benefit of connecting cells of low internal resistance in parallel.
`(iii) text(Mixed grouping)` In this combination, a certain number of cells are connected in various series and all such series are then connected in parallel. Number of cells `= mn`
emf of combination `= nE`
Total internal resistance `= (nr)/m`
Current taken in external resistance,
`i = (mnE)/( nr + mR)`
For maximum current in the circuit mR = nr.
If two cells oppose each other, then current taken from them `I = (E_1 -E_2)/(r_1 +r_2 +R)`
Similarly, if cells support each other, then `I = (E_1 +E_2)/(r_1 +r_2 +R)`
Charging current of a cell is given by
`i = text(emf of charger - emf of cell)/text(total resistance of the circuit)`
In a battery of N cells each of emf E, if n cells arc wrongly connected, then net emf,
`E' =NE - 2nE`