Electronics

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‘When did electronics branch out as a separate arm of electrics?’

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That could vary with location ( country) but here in  the USA it went like this. In the late 1920s  a  radio repairman was called a radiotrician. The term was patented in 1929. When you graduated the NRI course and passed the exam you became a Radiotrician. The FCC would award you a Radio Engineers license. This would be separate from the electrical field and would not qualify you to work in the electric field. So one answer would be 1929. The NRI course material is available here if you are interested:

http://www.americanradiohistory.com/Nati...o_1930.htm

Another answer could be based on the transition of Radio Age magazine to Electronic Age in 1957.
(The question here is, "Was radio electronics or did electronics begin about the time the first ICs appeared?".)

In 1929 radio was separated from electrics and in the 1950s electronics was separated from electrics. So there is no simple answer to the question. In the 1970 the electricians wanted no part of the computer so the ETs took them as a separate field. In the 1980s the electricians discovered the computer age was coming and wanted them back. I worked in an E&I shop and an I&E shop in the 1980s. In 2000 I worked as an Electrician doing electric, instrument  and computer.
So it went full circle. I graduated the NRI course in the '60s and became a radiotrician. In the '70s USAF made me an ET (avionics technician). In the '80s I worked on whatever the electricians couldn't or didn't want to. In the '90s I worked on everything electric or electronics under 13.8 Kv. (We do distinguish between outside electricians (linemen) and inside electricians (wiremen). Our apprentices are required to complete an electronics course in order to become journeyman electricians so the two have become one again.

I'm not sure I answered your question but maybe it's better than my first post. 
73