“Watt” (a unit of power) sounds like “what.” The joke has been cited in print since at least 1919.
 
“The same friend asked ‘what’s the unit of power?’, only to get confused when the teacher said ‘Yes, you’re right’” was posted on the newsgroup uk.rec.sheds on January 26, 1998. “In my physics exam today, a question asked ‘What’s the unit of power?’  I answered ‘Correct.’  #joke” was posted on Twitter by Dave J. Holloway on June 9, 2009.
 
   
Wikipedia: Watt
The watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In SI base units, the watt is described as kg⋅m2⋅s−3. The watt is named after James Watt, an 18th-century Scottish inventor.
     
Newspapers.com
29 May 1919, Morrison (OK) Transcript, pg. 2, col. 2:
Unit of Power.
Physics Teacher—Tell me, Frank, what is the unit of power?
Frank (suddenly waking up)—The what, sir?
Physics Teacher— Quite right.
 
Google Groups: uk.rec.sheds
Sheddy T-Shirts
Richard Lancashire
1/26/98
(...)
Is that something to do with loudspeakers? My friend once asked our Physics teacher why cheepers were small and woofters were big, I didn’t know Physics teachers could laugh that much.
 
The same friend asked “what’s the unit of power?”, only to get confused when the teacher said “Yes, you’re right.”
 
Twitter
Dave J. Holloway
@dajoho
In my physics exam today, a question asked “What’s the unit of power?”  I answered “Correct.”  #joke
6:47 AM · Jun 9, 2009·Twitter Web Client
 
Twitter
The Souls That Said No
@Snikoggs
In my physics exam today a question was asked “What’s the unit of power?” . . .
I answered “Correct.”
12:16 PM · Jul 13, 2011·Mobile Web
       
Twitter
𝘌𝘸𝘢𝘯 𝘞𝘢𝘥𝘦
@EwanWadeEsquire
My physics teacher asked me “What’s the unit of power?” I said “Correct.” #ScienceJokes
4:42 PM · Nov 27, 2011·Twitter Web Client
 
Twitter
Bob Kostic
@causticbob
In my physics exam today a question asked “What’s the unit of power?”
I answered “Correct.”
5:34 AM · Mar 21, 2012·TweetDeck
 
Twitter
Bob Kostic
@causticbob
In my physics exam today a question asked “What’s the unit of power?”
I answered “Correct.”
7:23 PM · Aug 17, 2020·Twitter Web App