This may be too obvious to write, but it depends on the person.
I can take a 5 minute nap (taking less than a minute or two to fall asleep), and I wake up fully refreshed.
My wife takes 15 minutes to go to sleep, and wakes up groggy regardless of how long she sleeps..
On the occasions when we might take a nap together, I have woken up and am ready to go before she is even able to get to sleep.
William Jefferson Clinton was noted for taking "power naps" in the Presidential Limo when he was being driven around DC for different engagements and meetings, and he claimed that it made it possible for him to work very long hours, productively.