Building up one weak arm...

Pretty much, yes. Generally you will always get slight imbalance I'm your arms, mine is my right being slightly stronger than my left.

One crucial tip, is if you're using dumbbells to curl, start with your weakest arm, then say if you get 2 sets of 10 and then you begin to struggle on your third set... You only manage 8 reps, always then match it with your stronger arm, don't go over, even though you can... Or this will obviously perpetuate the imbalance.

Also, make use of the ez bar to curl your arms simultaneously, over time, it should even out to a point that's it's no longer an issue.

I remember this exact problem when I started out, good luck

Do lots of dumbbell work to strengthen weak side. I do db chest press, single arm press, A press, preacher curls, oh db press. Always work weak arm first and at a weight you can do 3 sets at 8 -10 reps. Machine or barbell work means your strong side can take over limiting how hard the weak side has to work. I've also got weak right leg so do single leg work too. I'm not sure how long it takes to build up strength though, I've only been doing it a couple of weeks.