Cells In Parallel

Question

Three identical cells, each with internal resistance 0.6 ohm, are connected in parallel to reduce the effective source resistance, so what is their combined internal resistance?

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Identical cells connected in parallel keep the same overall emf as a single cell, but their internal resistances combine like resistors in parallel, giving $r_{eff} = \frac{r}{n}$ for $n$ identical cells, a concept covered in NCERT Class 12, Chapter 3 (Current Electricity). Here $r = 0.6$ ohm and $n = 3$, so $r_{eff} = \frac{0.6}{3} = 0.2$ ohm. Parallel grouping is used when a large current is required, since the reduced internal resistance lets the battery deliver more current. The option 1.8 ohm is wrong because it adds the three resistances as if the cells were connected in series, giving $3 	imes 0.6$ instead of dividing. The option 0.6 ohm ignores the parallel reduction entirely and simply reports a single cell's internal resistance. The option 0.3 ohm incorrectly divides by 2 instead of 3, perhaps from miscounting how many cells share the load. A plausibility check confirms the result: any parallel combination must be strictly smaller than a single branch value, and 0.2 ohm is indeed less than 0.6 ohm, fully consistent with three equal internal paths sharing the current and thereby lowering the effective resistance to one third.

Cells In Parallel

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