The researcher might need to find the largest N that can be enrolled, and work backwards from there to find an appropriate balance between alpha and beta. She may need to forgo the possibility of finding a small effect, and acknowledge that power will be adequate for a large effect only. When the number of cases in the two groups is uneven the effective N for computing power falls much closer to the smaller sample size than the larger one. Given an effect size, and alpha, and sample size, power is known. I error, the determination of a clinically important effect, the potential sample size, as well as the importance of identifying an effect, should one exist.
Some studies involve putting patients at risk.
At one extreme, the risk might involve a loss of time spent completing a questionnaire. At the other extreme, the risk might involve the use of an ineffective treatment for a potentially fatal disease. These issues are clearly beyond the scope of this discussion, but one point should be made here. Ethical issues play a role in power analysis. If a study to test a new drug will have adequate power with a sample of 100 patients, then it would be inappropriate to use a sample of 200 patients since the second 100 are being put at risk unnecessarily.