strong text In the answer to this question, it stated that the current would remain unchanged and I was wondering why the current would remain the same for the portion of the wire even though the radius has decreased which would restrict flow and therefore current. Any help much appreciated
In terms of particle electrons, consider a cross section of the wire. The number of electrons passing any cross section per unit time is the same - assuming that the electrons are not pooling up anywhere. For this to occur, the density of the electrons in the thinner section has to be greater than in the thicker section. Think in terms of the flow lines of the electrons down the wire - they have to bunch up to get through the thin section. Hence, the current density is greater in the narrow section. And heating is related to current density.
Alternatively, think of it as three resistors. A big resistance between two smaller resistances, in series. The current is conserved, so the current is the same in each resistor because it has no where to go to or come from other than the other resistors. The (linear) heating is proportional to resistance for a given current.
I was wondering why the current would remain the same for the portion of the wire even though the radius has decreased which would restrict flow and therefore current.
Electric current $i(t)$ through a surface is defined as the rate of charge transport through that surface, or
where $q(t)$ denotes instantaneous charge.
If the current through the "restricted" (decreased radius) cross sectional surface of wire was less than the current through the cross sectional surface of the wire before the restricted section, then charge would build up (accumulate) in the non restricted section.
Hope this helps