The bulk of the Cityrail suburban network had been electrified by the time the Harbour Bridge was opened in 1932. However, complete electrification would take a further 59 years (edit: thanks to Jim for pointing out my typo), occurring in bits an pieces with about one line being electrified every 10 years.
The next line to be electrified was the Carlingford Line. However, this happened in two stages: Clyde to Rosehill in 1936, then Rosehill to Carlingford (and Rosehill to Sandown) in 1959. I will cover the rest of the Carlingford Line as part of the 1959 electrification post. The line has dual tracks between Clyde and Rosehill, after which a single track continued North to Carlingford and another went East to Sandown through the industrial park. The first stage of electrification allowed electric trains to be run up to Rosehill station, which is adjacent to the Rosehill Racecourse, rather than having passengers have to take a steam train.
The Sandown Line and its 4 stations, used mostly by the workers along Grand Avenue in Camellia, would eventually be closed to passenger trains in 1990. Today it is used as a freight line, serving the warehouses and distribution centres. This portion of track has a level crossing, and there is usually a freight train that goes through there daily at around 6PM. If you happen to be driving along there at that hour, you can get stuck for about 20 minutes waiting for the freight train to pass. I know this from personal experience.
Post Script: Jim points out two things in the comments below. One is that Richmond was not electrified until 1991, making the period 59 year. I made a calculation error in working out the number of years between 1932 to 1991 and wrote down 49 years by mistake. This has now been corrected. The other is that as of 2010, freight trains no longer use the Sandown Line. I’ll have to take Jim at his word, though I will say that the last time I saw one on it was in mid 2009, which is consistent with what he says.