The internal resistance is normally taken as sensibly constant over one cycle of the normal discharge range of current.
The internal resistance does, however increase with ageing of the battery so the internal resistance after 500 cycles of a rechargeable has often increased enough to render the battery useless.
The internal resistance is independent of other circuit configurations, so long as the currents drawn are within the normal ratings.
The internal resistance increases with decreasing temperature, which is why it is harder to start a vehicle on a cold morning.
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