Parallel Combination of Cells:
(a) When e.m.f. and internal resistance is same for all cells : Suppose n cells of same e.m.f. E and internal resistance r are joined in parallel and this combination is connected with external resistance R as shown in the figure. All the cells are connected between junctions A and B. Any charge flowing in the circuit, passes only one cell. Therefore the equivalent e.m.f. = E = e.m.f. of one cell
The equivalent internal resistance
then the combination is significant.
(b) When the e.m.f. and internal resistance of the cells are different:
When the positive terminals of all cells are connected to one point and all their negative terminals to another point, the cells are said to be connected in parallel.
As shown in figure, suppose two cells of emf’s ε1 and ε2 and internal resistances r1 and r2 are connected in parallel between two points A and B
The end points of A and B are connected with external resistance R.
If in each cell current is I1 and I2 respectively then total current in external resistance is
I = I1 + I2 ……………… (1)
If terminal potential between A and B is V.
For I cell V = ε1 – I1r1 …………… (2)
For II cell V = ε2 – I12r2 ………….. (3)
From above equations.
If equivalent e.m.f. is εeq and equivalent internal resistance is req of combination then terminal potential difference will be
V = εeq – Ireq …………… (5)
Comparing equation (4) and (5),
By use of parallel combination it is clear:
(i) When ε1 = ε2 = ε and r1 = r2 = r means two cells of equal emf and equal internal resistance are connected in parallel then εeq = ε and req = \(\frac{r}{2}\)
(ii) When n cells of equal emf and equal internal resistance are connected in parallel combination
than εeq = ε and req = \(\frac{r}{n}\) then electric, current in external resistance will be
I = \(\frac{\varepsilon}{R+r / n}\) ………………….. (8)
(iii) We can display equations (6) and (7) in the below form
Similarly if n cells are combined in parallel system then,
