In the United States there are low power stations that are around 100 watts. They do not require a license. Laws about this vary from country to country.
Something else, power is money. A 10, 000 AM or FM station at 220VAC will use 45 amps, more than most houses. Ask your parents how much their electric bill is to get an idea how much that cost.
None of this power actually goes to capacitor. A LC tank circuit helps clean up the signal so you are not trashing the other stations.