# Grouping of Cells

(i) Cells in Series

(ii) Cells in Parallel

(iii) Mixed Grouping

### Cells in Series:

When ‘n’ identical cells each of EMF ‘E’ and internal resistance ‘r’ are connected in series to an external resistance ‘R’, then

total emf of the combination = n E

effective internal resistance = n r

Total Resistance = R + nr

Current through external resistance

$\large i = \frac{n E}{R + n r}$

If R << n r then $\large i = \frac{E}{r}$ = current from one cell

If R >> n r then  $\large i = \frac{nE}{R}$

Wrongly Connected Cells :

(a)By mistake if ‘m’ cells out of ‘n’ cells are wrongly connected to the external resistance ‘R’

(b)total emf of the combination = (n – 2m)E

(c)total internal resistance = n r

(d)total resistance = R + n r

(e)current through the circuit $\large i = \frac{(n-2m)E}{R+nr}$

### Cells in Parallel:

When ‘n’ identical cells each of EMF ‘E’ and internal resistance ‘r’ are connected in parallel to an external resistance ‘R’, then

Total emf of the combination = E

effective internal resistance = r/n

total resistance in the circuit $\large = R + \frac{r}{n}$

Current through the external resistance $\large i = \frac{E}{R + \frac{r}{n}} = \frac{nE}{nR + r}$

If R >> r/n, then i=E/R = current from one cell.

If R << r/n, then i = nE/r

### Mixed Grouping:

If n identical cell’s are connected in a row and such m rows are connected in parallel as then

Equivalent emf of the combination Eeq = nE

Equivalent internal resistance of the combination $\large r_{eq} = \frac{nr}{m}$

Main current flowing through the load $\large i = \frac{nE}{R +\frac{nr}{m} } = \frac{m n E}{mR + nr}$

ondition for maximum power $\large R = \frac{nr}{m}$