Considerable interest exists in the possibility of exploiting strong tidal currents as a source of renewable energy. Methods to understand and evaluate this resource have been developed for simple flow configurations, such as a tidal channel linking the open ocean to an inner basin. More complicated flow geometries involving branching channels have been considered recently. A simple prototype for this class of problem consists a tidal channel that is split by an island into two sub-channels. In-stream energy conversion devices are deployed in one of the sub-channels, while the second is left free for navigation or other purposes. The free sub-channel allows flow to be diverted away from the impeded sub-channel, which may lead to a reduction in the available power. In the present paper, an electric circuit analogue is used to develop a linear theory for the power potential of a split tidal channel. Although limited to linear friction, this approach allows for inclusion of the effects of flow acceleration and finite basin size that have not been considered previously. Based on the equivalent circuit, analytical expressions are derived for the maximum extractable power and for the modification of the flow in each section of the channel at maximum power. Extension of the theory to multiple branching channels is discussed. Results for a few simple cases are considered. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.