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Explain how the cells are grouped in parallel. Obtain the condition for maximum current through an external resistor. |
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Answer» Solution :Cells in parallel. The cells are said to be connected in parallel, if we can proceed from one point to another through different paths. Fig. shows the parallel combination of m cells. Here m cells, each of e.m.f. E and internal resistance R are connected to an external resistance R. In parallel combination, the total e.m.f. of the cells is equal to the e.m.f. of a single cell. `therefore ` Total e.m.f. of the cells=E Since internal resistances of all the cells are connected in parallel. `therefore ` Total internal resistance of the cells is GIVEN by `(1)/(r.)=(1)/(r)+(1)/(r)+ . . . .+m` TIMES or `(1.)/(r.)=(m)/(r)` `therefore r.=(r)/(m)` . So current flowing through the circuit `I=(E)/(R+(r)/(m))` Case 1. if `R GT gt (r)/(m)`, so `R+(r)/(m)=R` `therefore I=(E)/(R)=`current due to single cell. Case 2. if `R lt lt (r)/(m)`, so `R+(r)/(m)=(r)/(m)` `therefore I=(E)/((r)/(m))=(mE)/(r)` `=mxx`current due to single cell.  Thus in parallel combination of cells, to have maximum current, the total external resistance of the circuit should be negligible as compared to the total internal resistance of the cells. |
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