If a miner solves the problem in less than one second then how does it use the extra capacity.
The resolution of the timestamp in a Bitcoin block header is one second. However, if a miner should find a valid proof-of-work and create a valid block, they do not have to wait one second before starting work on a new block. It is perfectly legal for two successive blocks to have identical timestamps. In fact, it is legal for the succeeding block to have a timestamp that is earlier than that of the preceding block by up to 7200 seconds. See Why is two hours the maximum acceptable offset for Bitcoin blocks?
So a miner can immediately start work on a new block, and this is normally what they actually would do. Hence there is no "excess capacity" at all.
It is very hard to find the correct answer but verifying the answer is instant and you need that answer to begin to mine the next block, so as soon as a miner receives one answer that he can verify is valid he will take that information and use it to try to find the next answer without loosing time and because every other miner will do the same.
It will use it to solve the next problem.