We consider a multiple-access channel where the users are powered from batteries having non-negligible internal resistance. When power is drawn from the battery, a variable fraction of the power, which is a function of the power drawn from the battery, is lost across the internal resistance. Hence, the power delivered to the load is less than the power drawn from the battery. The users consume a constant power for the circuit operation during transmission but do not consume any power when not transmitting. In this setting, we obtain the maximum sum-rates and achievable rate regions under various cases. We show that, unlike in the ideal battery case, the TDMA (time-division multiple access) strategy, wherein the users transmit orthogonally in time, may not always achieve the maximum sum-rate when the internal resistance is non-zero. The users may need to adopt a hybrid NOMA-TDMA strategy which combines the features of NOMA (non-orthogonal multiple access) and TDMA, wherein a set of users are allocated fixed time windows for orthogonal single-user and non-orthogonal joint transmissions, respectively. We also numerically show that the maximum achievable rate regions in NOMA and TDMA strategies are contained within the maximum achievable rate region of the hybrid NOMA-TDMA strategy.