In this paper, we address simultaneous estimation problems (SEPs) of state and physical parameters of rechargeable batteries. In general, the problems are transformed to state estimation of an augmented system whose state includes the parameters of the original system. Then, the SEPs are commonly solved by estimating the state of the augmented system. As a drawback of the solution, the simultaneous estimation fails for some types of the input currents. In this paper, we attempt to find input current conditions such that the SEPs are theoretically solved, through observability analysis of the augmented system.