Who invented the first electric guitar on 1935?

USA: At the NC State Engineering Fair in 1940, first prize went to NCSU physics professor Sidney Wilson for his invention of the world's first fully electric guitar. The instrument was also the first to have single-string pick-up. Clearly the sensation of the fair, the guitar was played by physicist Mickey May.

The Gibson Corporation had introduced a converted acoustic guitar - the ES-150 - in 1937 that used a single bar to pick up the signal from all strings. The instrument achieved some popularity, but was plagued by unequal loudness across the six strings.

http://www.physics.ncsu.edu/history/guitar.html