Out in the turbo the other night and i wasnt aware that i was being followed by the undercover traffic police for about 10 miles.The 'apparently' saw me braking hard comming into a roundabout and decided to follow me(Obviously to try and do me for speeding

)but even as i stayed well within the speed limits they pulled me anyway and when they did they noticed my front number plate and fined me £30

Fair play i suppose,but..
When i went back to my car the thing wouldnt start so had to wait for ages down some dodgy back road untill my mate came and saved me

Battery was totally dead,so what could it be?
When i start ther car the volts go up to 13v and when the fan's cut in it takes it down to about 10.5-11v

And when at low rev's the battery light is on faintly?
So chap's.Battery or alternator?Bering in mind ive started the car from a flat battery 3 times in a row..
Cheers