You only receive 10% of a cities potential income if you do not own the capital city.
When you own a capital city, you receive 100% of the cities income that you have captured in the same country.
When you own all the cities in a country you receive an extra 10% income bonus on all cities in that country. Bear in mind collateral damage which affects the population will also have an adverse effect on the income.
----
intelligence + imagination = extraordinary result