Left hand is more trained

[Eugene]

I'v trained for about 6 weeks now, and the result is that my biceps and triceps are stronger and larger in the right arm, even tho I trained equally both hands.

Therefore I'd like to train my left hand more.
In my gym there aren't enough dumbells, so sometimes I must use barbells.
However I am afraid that when I use the barbell, my right arm makes up for the weaker left, and in fact they lift different weights.
My question is, is that assupmption correct, and if it is, is it ok to put more weight on the left side of the barbell?

 

[Tommy]

Im far from being an expert but six week's training isn't a long time, this sport takes time and patience,for myself though the weaker side caught up eventually when I focused more on the compound lifts.In time it will even out for you

 

[BIGDAVE]

Yeah,as Tommy said it should eventually even out.6 weeks is no time in this sport,so give it time and dont expect too much too soon.