This paper uses Fisher information to quantify the identifiability of internal resistance and charge capacity for a first-order nonlinear equivalent-circuit model of a lithium-ion battery undergoing periodic cycling. The paper derives analytic Cramér-Rao bounds on the variances with which a maximum-likelihood estimator can determine these parameters in the presence of white and Gaussian voltage measurement noise. This mathematical analysis shows that the challenge of battery parameter identifiability, already recognized in the literature for higher-order electrochemical battery models, is fundamentally present even for much simpler equivalent circuit models. The analysis also quantifies the degree to which the sensitivity of battery open-circuit voltage with respect to state of charge affects parameter identifiability. The paper serves as a first-cut analysis of the accuracy with which one can determine two battery state-of-health metrics - namely, power and capacity fade - from periodic cycling tests.