Question

Illustrate-combination of cells e.g., three cells, in parallel, explaining the combination briefly. Obtain an expression for current ‘i’ in the combination.

Answer 1

Combination of cells in parallel: Let there be n cells, each of e.m.f. E and internal resistance r, be connected in parallel as shown in the diagram.
Total e.m.f. across the point A and B is E

Total internal resistance 

`1/"r"_1 = 1/"r" + 1/"r" + 1/"r".... = "n"/"r"` (if there are n cells)

or  r₁ = `"r"/"n"`

But total resistance of circuit = R + `"r"/"n" = ("nR" + "r")/"n"`

∴ Current i = `"Total e.m.f"/"Total resistance"`

`= "E"/("R" + "r"/"n")`

`= "nE"/("nR + "r"")`

It is advantageous to join cells in parallel when the internal resistance of each cell is quite high as compared to the external resistance R.

Then, Approximately, i = `"nE"/"r"` (neglecting R).