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I was solving a particular question which landed me to a position where I have to decide whether the following ring expansion would take place or not by carbocation rearrangement:

carbocation shift

If the expansion takes place, then Bromine(an electronegative element) would apply -I effect on carbocation and will make it unstable but also 5 membered ring is more stable than 4 membered ring due to less angle strain.
How to decide it then?

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Stability is a combination of all factors, weighted towards their contribution to the overall $\Delta G$. In this case ring strain is a major issue, and one not necessarily likely to win out over the tertiary -> secondary carbocation transition you've drawn (the bromine has a lesser role to play as well, as you highlight). An equilibrium will form between two drawn structures. Absent modeling I can't give hard numbers, but my intuition is that the cyclopentane will be the more stable.

Ultimately though you're missing the greatest contributor to a beneficial $\Delta G$: quenching the carbocation. Whether or not you get a cyclopentane/cyclopentene is going to depend on how quickly a proton can eliminate from those methyl groups to form a terminal alkene. In most cases I think the 1,3-carbon shift is going to be faster, but not by much when there's six potential protons that can eliminate.

As with most carbocation systems you're going to get a mix of products.

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