This solution also worked for me.
My problem was that the c920 would show up in OBS only under default settings, which looked like SD video.
I had installed the latest Logitech Gaming Software which recognized and seemed to control both my c920 and my 922. The 922 was working fine but not the 920.
When I looked at the driver details in the Device Manager in Windows 10, I found both the 920 and 922 uncer Cameras, but the 920 had a driver dated from 2006.
When I selected the automatic driver update, it said I had the newest one.
After finding this thread, I went back to the Logitech Support site and finally found the correct driver.
http://support.logitech.com/en_sg/downloads
Go all the way down to "Logitech Webcam Software" and make sure the version numbers are as above.
Finally I can access the 920 in OBS and change the settings to HD without it freezing/disappearing.
Strangely, after the installation of the new driver, the 920 no longer appears under Cameras in the Device Manager, but instead it's under Imaging Devices.
Weird.