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Why is the internal resistance of a cell not constant?

Ans. This can also answer to the question that "Why  internal resistance of battery increases with usage "?

The internal resistance depends on the concentration and mobility of the ions present in the liquid or paste, and on the surface-resistance of the internal 'plates'.

Over time, due to chemical reactions, the ionic concentrations reduces. And you get deposition of high resistance materials (e.g. insoluble sulphates) on the plate surfaces. Both of these increase internal resistance.

There are many types of cell so the exact chemical changes depends on the cell-chemistry.

For more details, you could try asking under Chemistry, as battery-chemistry is a fairly specialist area.

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