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Suppose I have a source of emf E connected in series with a resistor R. The loop rule suggests that the current through the resistor is i = V/R.

Now consider a parallel system of two sources of emf, connected in series with a resistor. Application of the loop rule to a loop through either source suggests that the current through the resistor is i = V/R. If I now replace one source with low resistance wire, then very little current will pass through the resistor, and yet the loop rule still suggests that the current through the the resistor is i = V/R?

What am I missing here?

Thanks

James