That isn't a simple question to answer. It should work on most graphics cards with DVI, but will not work on those with HDMI. There are also potential problems with the RGB end. First, I'll attempt to explain a little about DVI.
Old computers and monitors use VGA connectors, which is an analogue video connector. Modern TVs usually use HDMI, which is a digital video and audio connection. Pretty straight-forward so far. Now DVI is techically not one type of connector, but 3; DVI-A, DVD-D and DVI-I. DVI-A is essentially a VGA cable with a DVI connector. DVI-D is basically the video portion of HDMI with a DVI connector. DVI-I is BOTH. That cable is DVI-A, so will only work with DVI-A (rare as an output and usually only used for converters like this) and DVI-I connectors. There is a good chance that your graphics card has a DVI-I connector, but it is possible that it is DVI-D. If it was supplied with a DVI-VGA adapter dongle or you have used it with one before it's a pretty safe bet that it's DVI-I, so you're good to go at that end. As it's a Radeon 4850 it seems pretty likelly it's DVI-I as a review I saw for it had such adapters bundled.
The other end could also be a problem though. That cable states that it is RGB component; that is each of the connectors represents either the
Red
Green or
Blue part of the video signal, presumably with the sync signal mixed into the green cable. The way VGA and related standards work is that there is a red, green, blue, vertical sync and horizontal sync signals. Now RGB component can be in three forms: RGB + H + V (5 cables), RGB + C-sync* (4 cables) or RGB with C-sync mixed into the green connector (3 cables). Now if your TV or amp has RGB component, it has to be in the correct format (i.e. the right number of cables) or it won't work and you'll need a separator to separate the signals.
*C-sync = composite sync i.e. the horizontal and vertical sync mixed together.
There is another complication though - the component on your TV/amp is FAR more likelly to be YPbPr and not RGB. YPbPr is a far more common type of component video and you'd need a pretty hefty converter to convert between the two.
However, there may be another way - your graphics card can nativelly output a component signal. Check to see if you have a cable like the one below somewhere. It chould have what looks like an s-video connector on the end (it is actually a video-card multi-out), and just plugs into the corresonding port on your graphics card. You will probably have to tell the graphics card to use it, but thats pretty simple.
EDIT: oops, here's the pic: