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