The heated screen is in 2 halves as you know and they are loads of little wires that are basically arranged the same way as a light bulb, you add live to 1 side of the wire and ground to the other, the power shorts out through the wires and causes them to heat up in the same way as a light bulb does. It never gets that hot though at best you'll feel warmth on the screen but even cool to touch its enough to melt frost /mist.
To test you'll remove the A pillar trim and find the 2 spade terminals, 1 will be upper and 1 will be lower, they are the only bit that connects to a riband that comes off the glass. If you put a multimeter to them you'll see a voltage when the screen is on.
If no voltage and the screen is on then there's a fault at the relay or fuse or wiring. If voltage but no screen then there is damage to the screen.
Note.
I haven't studied the screen other than I have seen the elements inside and they all collect at the riband so I see clearly how it works, the bit I don't understand is 2 fold. The fault would be a break in the circuit you'd expect but then why does it result in total failure? Are the elements collectively joined at the riband in such a way that if 1 melts it causes a short to the others resulting in complete failure? Seems a bit rubbish that, why not have the odd element go down but it still works? I hardly think that the elements would melt inside the glass surely? But that wouldn't cause complete failure either.
Ah well.
56 350 2.2 130ps mk7 with 2 side doors
65 290 2.2 125ps custom with 2 side doors
07 350 170ps
Ids v86 licence + v86.04 update + xprog
hereIds map
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