Question

In lecture 8 dealing with dependent sources and amplifiers, Prof. Agarwal showed that if the current controlled source has an equation of i=k/Vr, we can deduce Vr=(KR)^1/2. Assuming the values of K=R=1, we get Vr=1V. There is V in the ckt despite of no independent source since initially Vr is 0 and the moment I increases, Vr also increases and they balance out each other to 1V. Can the same derivation for Vr be applied if i=K*Vr(squared)? Will the logic work? Since we get Vr=1/KR, if K=R=1, Vr=1. But logically Vr is 0 indefinitely since no independent source is present. Which one is true?