Here v has a different potential than Vs relative to the ground. V1 can be expressed in terms of V, that is V1=V/3.Decide v as a function of Vs.
I would like to solve this using KVL, if possible. I tried, and got this (for three loops):
i*2R+v1+i3*3R-Vs=0
-4V1+i2*3R+Vs-i3*3R=0
i*2R+V1-4V1+i2*3R=0
(i being the left side current, i3 middle and i2 right). Is this KVL loop analaysis correct?