Im going to buy 1GB AMD 7770 graphic for its low power consumption, but if i buy a 2GB 7770 card, then will its power consumption increase or remain same? 
having a doubt?
The increase will be marginal. But why pay extra for an unnecessary 1 GB. 2 GB for an HD 7770 is overkill and I am not sure if 2 GB models are available or not.
@ OP - if you need a 2GB gfx card get nothing less than HD7850 2GB @ ~16.5k
@op 2 gb is just too much for that GPU. It won't be able to utilise that much. Stick to the 1 gb version 
Doubt answered.
2 GB in a HD 7770 is a waste. Power consumption will BARELY increase.
HD 7850 should be the minimum for 2 GB VRAM.
Closing.
2 GB in a HD 7770 is a waste. Power consumption will BARELY increase.
HD 7850 should be the minimum for 2 GB VRAM.
Closing.