External web cam produces no video
I have a Logitech Brio 500 webcam. When I plug it in, it shows up in the video menu of both FaceTime and PhotoBooth, but the picture is black. If I switch to the built-in camera, then I get a picture. If I move the webcam to a Windows machine, it works fine. What could be blocking the video, but letting me pick it in the video menus?
MacBook Pro 13″, macOS 10.12