It really took off with mechanical clocks in the 17th century, and has been making steady progress ever since, but with few dramatic breakthroughs. The first commercial use for electricity was the telegraph, which appeared just before the Civil War. Useful motors and generators date from the late 19th century. The vacuum tube was invented early in the 20th century, the transistor a few decades later, and the integrated circuit shortly thereafter. Larger and larger scale integrated circuits continue to appear, but these are only the most conspicuous peaks of the enormous icebergs of the electrical art.
Success breeds success and failure breeds failure.
Both are exponential. Another result of the electrical success is that the field is competitively more attractive to the best students, who, in turn, accelerate its achievements. Multiple electric motors replaced line shafting to drive different machines, and they replaced mechanical power transmissions to drive different portions of the same machine. Electrical instrumentation and control has almost completely replaced mechanical instrumentation and control. Centrifugal governors, steam engine indicators, and pneumatic process controls are either gone or are on their way out.