In the U.S. House of Reps.
When California gains a representative, then another state must have what?
How often can the number of representatives be adjusted? After a what?
http://ballotpedia.org/United_States_House_of_Representatives
Read carefully, especially the sections BELOW the map.
In the U.S. House of Representatives, when California gains a representative, it means that the population of California has increased enough to warrant an additional seat in Congress. The number of representatives in the House is determined by the apportionment process, which is based on the population of each state.
Now, to answer your second question, the number of representatives in the House can be adjusted every 10 years after the decennial census. The decennial census is conducted by the U.S. Census Bureau and counts the population of the country. It is used to determine the distribution of seats in the House among the states based on population changes.
After each census, the seats in the House are reapportioned among the states to reflect changes in population. If a state's population has increased relative to other states, it may gain additional seats. On the other hand, if its population has decreased or grown at a slower rate, it may lose seats.
So, to summarize, when California gains a representative, it means that its population has increased. The number of representatives can be adjusted every 10 years after the decennial census, which determines the distribution of seats in the House based on population changes.