An analogy is drawn between the flow through multiple, frictional straits and the current through combinations of resistors acting in series and parallel in an electrical circuit. Kirchoff's laws are replaced by continuity of mass and the generalized island rule [Wajsowicz, 1993a]. Expressions are derived for the equivalent resistance of straits acting in series and in parallel. Hence the total “current” can be calculated for a given “voltage” supplied by the wind stress curl over the adjacent ocean basin. The model may be used to help understand how to parameterize the effect of the many islands within the Indonesian archipelago in a numerical general circulation model by combining islands/straits into resolvable groups with the same effective resistance. For example, from the expression for parallel straits it can be deduced that if there is at least one gap at each latitude within the archipelago, which is wide and deep enough not to block the throughflow, then the throughflow achieves its predicted wind-driven maximum. The transport is not carried by the largest gap, but, instead, is carried by the westernmost gap up to a friction-determined limit, and so on eastward, until a dynamically wide gap is reached. This gap carries the remainder of the transport; gaps to the east carry no transport. Hence the model explains surprising recent observations that the throughflow is as large as the Sverdrup model prediction of O (15 Sv). It also explains observations that the narrow, shallow Lombok and Savu Straits to the west carry significant transport, even though Timor Strait to the east is much wider and deeper, and similarly for Makassar Strait versus Molucca Strait.